diff --git a/src/change.rs b/src/change.rs
index e29b3cf..c1526d3 100644
--- a/src/change.rs
+++ b/src/change.rs
@@ -55,10 +55,31 @@ pub enum ChangeComparison {
 
 #[derive(Debug)]
 pub enum ChangeClass {
+    /// This change is backward incompatible. A client on the old version may
+    /// not be able to communicate with a server on the new version.
+    ///
+    /// This represents an input type becoming more restricted (so an old client
+    /// can send request data that a new server will reject), or an output type
+    /// becoming less restricted (so a new server can send response data that an
+    /// old client will reject).
     BackwardIncompatible,
+    /// This change is forward incompatible. A server on the old version may
+    /// not be able to communicate with a client on the new version.
+    ///
+    /// This represents an input type becoming less restricted (so a new client
+    /// can send request data that an old server will reject), or an output type
+    /// becoming more restricted (so an old server can send response data that a
+    /// new client will reject).
     ForwardIncompatible,
+    /// This change is bidirectionally incompatible. A server on the old version
+    /// may not be able to communicate with a client on the new version, and
+    /// vice versa.
     Incompatible,
+    /// This change is trivial (e.g., metadata changed). Servers and clients
+    /// across versions will not be affected.
     Trivial,
+    /// This change is not handled by `drift` yet, and it should be assumed to
+    /// be bidirectionally incompatible.
     Unhandled,
 }
 
diff --git a/src/schema.rs b/src/schema.rs
index 133c978..044943f 100644
--- a/src/schema.rs
+++ b/src/schema.rs
@@ -17,6 +17,21 @@ pub(crate) enum SchemaComparison {
     Output,
 }
 
+/// Controls whether effective nullability should be checked at this point.
+///
+/// Effective nullability is a property of the entire schema ref chain
+/// (wrapper.nullable || inner.effective_nullable). We check it once at
+/// comparison entry points (response schemas, request bodies, properties, etc.)
+/// but not when traversing through wrapper structures.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+enum EffectiveNullableCheck {
+    /// This is a comparison entry point; check effective nullability.
+    Entry,
+    /// We're traversing through a wrapper; effective nullability was already
+    /// checked at the entry point.
+    WrapperTraversal,
+}
+
 impl From<SchemaComparison> for ChangeComparison {
     fn from(value: SchemaComparison) -> Self {
         match value {
@@ -37,6 +52,11 @@ impl Compare {
         Ok(())
     }
 
+    /// Compare two schema references. This is the main entry point for schema
+    /// comparison, used for response schemas, request bodies, properties, array
+    /// items, etc.
+    ///
+    /// Always checks effective nullability at this level.
     fn compare_schema_ref_helper(
         &mut self,
         dry_run: bool,
@@ -44,6 +64,32 @@ impl Compare {
         old_schema: Contextual<'_, &ReferenceOr<Schema>>,
         new_schema: Contextual<'_, &ReferenceOr<Schema>>,
     ) -> anyhow::Result<bool> {
+        self.compare_schema_ref_inner(
+            dry_run,
+            comparison,
+            EffectiveNullableCheck::Entry,
+            old_schema,
+            new_schema,
+        )
+    }
+
+    /// Inner implementation of schema ref comparison with explicit nullable
+    /// check control.
+    fn compare_schema_ref_inner(
+        &mut self,
+        dry_run: bool,
+        comparison: SchemaComparison,
+        nullable_check: EffectiveNullableCheck,
+        old_schema: Contextual<'_, &ReferenceOr<Schema>>,
+        new_schema: Contextual<'_, &ReferenceOr<Schema>>,
+    ) -> anyhow::Result<bool> {
+        // At entry points, check effective nullability before any structural
+        // comparison. This handles nullable changes through wrapper chains.
+        if nullable_check == EffectiveNullableCheck::Entry {
+            let _ =
+                self.compare_effective_nullable(dry_run, comparison, &old_schema, &new_schema)?;
+        }
+
         // Handle single-element wrappers: allOf/anyOf/oneOf with one item.
         // These are semantically equivalent to their inner type.
         //
@@ -55,11 +101,11 @@ impl Compare {
             Ok(result)
         } else {
             // General path: resolve and compare.
-            let (old_schema, old_context) = old_schema.contextual_resolve()?;
-            let (new_schema, new_context) = new_schema.contextual_resolve()?;
+            let (old_resolved, old_context) = old_schema.contextual_resolve()?;
+            let (new_resolved, new_context) = new_schema.contextual_resolve()?;
 
-            let old_schema = Contextual::new(old_context, old_schema.as_ref());
-            let new_schema = Contextual::new(new_context, new_schema.as_ref());
+            let old_schema = Contextual::new(old_context, old_resolved.as_ref());
+            let new_schema = Contextual::new(new_context, new_resolved.as_ref());
 
             self.compare_schema(comparison, dry_run, old_schema, new_schema)
         }
@@ -93,7 +139,8 @@ impl Compare {
                 },
             ) => {
                 // Both old and new are single-element wrappers.
-                if old_meta != new_meta {
+                // Effective nullability is checked at the entry point, not here.
+                if has_non_nullable_metadata_diff(old_meta, new_meta) {
                     self.push_change(
                         "schema metadata changed",
                         old_schema,
@@ -105,8 +152,12 @@ impl Compare {
                 }
                 let old_inner = old_schema.append_deref(old_inner, "0");
                 let new_inner = new_schema.append_deref(new_inner, "0");
-                Ok(Some(self.compare_schema_ref_helper(
-                    dry_run, comparison, old_inner, new_inner,
+                Ok(Some(self.compare_schema_ref_inner(
+                    dry_run,
+                    comparison,
+                    EffectiveNullableCheck::WrapperTraversal,
+                    old_inner,
+                    new_inner,
                 )?))
             }
             (
@@ -117,11 +168,8 @@ impl Compare {
                 BareRef | InlineType,
             ) => {
                 // Old is a single-element wrapper, new is a bare ref or inline
-                // type.
-                //
-                // A bare ref or inline type does not have metadata, so if the
-                // old metadata is non-default, report a trivial change.
-                if has_meaningful_metadata(old_meta) {
+                // type. Effective nullability is checked at the entry point.
+                if has_meaningful_non_nullable_metadata(old_meta) {
                     self.push_change(
                         "schema metadata removed",
                         old_schema,
@@ -132,9 +180,10 @@ impl Compare {
                     );
                 }
                 let old_inner = old_schema.append_deref(old_inner, "0");
-                Ok(Some(self.compare_schema_ref_helper(
+                Ok(Some(self.compare_schema_ref_inner(
                     dry_run,
                     comparison,
+                    EffectiveNullableCheck::WrapperTraversal,
                     old_inner,
                     new_schema.clone(),
                 )?))
@@ -147,11 +196,8 @@ impl Compare {
                 },
             ) => {
                 // Old is a bare ref or inline type, new is a single-element
-                // wrapper.
-                //
-                // A bare ref or inline type does not have metadata, so if the
-                // new metadata is non-default, report a trivial change.
-                if has_meaningful_metadata(new_meta) {
+                // wrapper. Effective nullability is checked at the entry point.
+                if has_meaningful_non_nullable_metadata(new_meta) {
                     self.push_change(
                         "schema metadata added",
                         old_schema,
@@ -162,9 +208,10 @@ impl Compare {
                     );
                 }
                 let new_inner = new_schema.append_deref(new_inner, "0");
-                Ok(Some(self.compare_schema_ref_helper(
+                Ok(Some(self.compare_schema_ref_inner(
                     dry_run,
                     comparison,
+                    EffectiveNullableCheck::WrapperTraversal,
                     old_schema.clone(),
                     new_inner,
                 )?))
@@ -179,6 +226,62 @@ impl Compare {
         }
     }
 
+    /// Compare effective nullability of two schema references.
+    ///
+    /// Effective nullability is `wrapper.nullable || inner.effective_nullable`
+    /// for single-element wrappers, or just `schema.nullable` for terminal
+    /// schemas.
+    ///
+    /// This is called at comparison entry points (response schemas, request
+    /// bodies, properties, etc.) to detect nullable changes through wrapper
+    /// chains.
+    fn compare_effective_nullable(
+        &mut self,
+        dry_run: bool,
+        comparison: SchemaComparison,
+        old_schema: &Contextual<'_, &ReferenceOr<Schema>>,
+        new_schema: &Contextual<'_, &ReferenceOr<Schema>>,
+    ) -> anyhow::Result<bool> {
+        use EffectiveNullability::*;
+
+        let old_nullable = get_effective_nullable(old_schema)?;
+        let new_nullable = get_effective_nullable(new_schema)?;
+
+        let (message, class, details) = match (old_nullable, new_nullable) {
+            (NotNullable, NotNullable) | (Nullable(_), Nullable(_)) => {
+                return Ok(true);
+            }
+            (NotNullable, Nullable(kind)) => {
+                // non-nullable → nullable
+                let message = match kind {
+                    NullabilityKind::Wrapper => "nullable added at wrapper",
+                    NullabilityKind::Direct => "schema became nullable",
+                };
+                let class = match comparison {
+                    SchemaComparison::Input => ChangeClass::ForwardIncompatible,
+                    SchemaComparison::Output => ChangeClass::BackwardIncompatible,
+                };
+                (message, class, ChangeDetails::LessStrict)
+            }
+            (Nullable(kind), NotNullable) => {
+                // nullable → non-nullable
+                let message = match kind {
+                    NullabilityKind::Wrapper => "nullable removed from wrapper",
+                    NullabilityKind::Direct => "schema became non-nullable",
+                };
+                let class = match comparison {
+                    SchemaComparison::Input => ChangeClass::BackwardIncompatible,
+                    SchemaComparison::Output => ChangeClass::ForwardIncompatible,
+                };
+                (message, class, ChangeDetails::MoreStrict)
+            }
+        };
+
+        self.schema_push_change(
+            dry_run, message, old_schema, new_schema, comparison, class, details,
+        )
+    }
+
     fn compare_schema(
         &mut self,
         comparison: SchemaComparison,
@@ -206,54 +309,18 @@ impl Compare {
             return Ok(*equal);
         }
 
-        // We expand structures to ensure we don't accidentally fail to examine
-        // a field.
         let Schema {
-            schema_data:
-                SchemaData {
-                    nullable: old_nullable,
-                    read_only: old_read_only,
-                    write_only: old_write_only,
-                    deprecated: old_deprecated,
-                    external_docs: old_external_docs,
-                    example: old_example,
-                    title: old_title,
-                    description: old_description,
-                    discriminator: old_discriminator,
-                    default: old_default,
-                    extensions: old_extensions,
-                },
+            schema_data: old_schema_data,
             schema_kind: old_schema_kind,
         } = old_schema.as_ref();
         let Schema {
-            schema_data:
-                SchemaData {
-                    nullable: new_nullable,
-                    read_only: new_read_only,
-                    write_only: new_write_only,
-                    deprecated: new_deprecated,
-                    external_docs: new_external_docs,
-                    example: new_example,
-                    title: new_title,
-                    description: new_description,
-                    discriminator: new_discriminator,
-                    default: new_default,
-                    extensions: new_extensions,
-                },
+            schema_data: new_schema_data,
             schema_kind: new_schema_kind,
         } = new_schema.as_ref();
 
         // Examine properties that don't affect the serialized form.
-        let metadata_equal = old_read_only == new_read_only
-            && old_write_only == new_write_only
-            && old_deprecated == new_deprecated
-            && old_external_docs == new_external_docs
-            && old_example == new_example
-            && old_title == new_title
-            && old_description == new_description
-            && old_discriminator == new_discriminator
-            && old_default == new_default
-            && old_extensions == new_extensions;
+        // Nullability is checked at entry points via compare_effective_nullable.
+        let metadata_equal = !has_non_nullable_metadata_diff(old_schema_data, new_schema_data);
 
         if !metadata_equal {
             let _ = self.schema_push_change(
@@ -267,7 +334,13 @@ impl Compare {
             );
         }
 
-        let nullable_equal = old_nullable == new_nullable;
+        // Note: we do not report nullability changes here. They're instead
+        // reported in compare_schema_ref_inner (which knows how to perform
+        // recursion). But we use nullable_equal in the self.visited set. (To be
+        // honest, this seems a bit dubious. But does self.visited.insert even
+        // need to carry information about whether schemas are equal?)
+        let nullable_equal = old_schema_data.nullable == new_schema_data.nullable;
+
         let schema_equal = self.compare_schema_kind(
             comparison,
             dry_run,
@@ -866,8 +939,174 @@ fn classify_schema_ref(schema_ref: &ReferenceOr<Schema>) -> SchemaRefKind<'_> {
     }
 }
 
-/// Check if schema_data has any non-default values that would constitute
-/// metadata worth preserving.
-fn has_meaningful_metadata(data: &SchemaData) -> bool {
-    *data != SchemaData::default()
+/// Result of computing effective nullability.
+///
+/// For single-element wrappers, effective nullability is
+/// `wrapper.nullable || inner.effective_nullable`. For terminal schemas,
+/// it's just `schema.nullable`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+enum EffectiveNullability {
+    /// The schema is not effectively nullable.
+    NotNullable,
+    /// The schema is effectively nullable, with the source indicating where
+    /// the nullability comes from (outermost source if multiple).
+    Nullable(NullabilityKind),
+}
+
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+enum NullabilityKind {
+    /// Direct schema has `nullable: true` (e.g., `{ "type": "string", "nullable": true }`).
+    Direct,
+    /// Single-element wrapper has `nullable: true` in its metadata.
+    Wrapper,
+}
+
+/// Compute the effective nullability of a schema reference.
+fn get_effective_nullable(
+    schema_ref: &Contextual<'_, &ReferenceOr<Schema>>,
+) -> anyhow::Result<EffectiveNullability> {
+    match schema_ref.as_ref() {
+        ReferenceOr::Reference { .. } => {
+            // Bare ref: resolve and delegate to the schema handler.
+            let (resolved, context) = schema_ref.contextual_resolve()?;
+            let schema = Contextual::new(context, resolved.as_ref());
+            get_effective_nullable_for_schema(&schema)
+        }
+        ReferenceOr::Item(schema) => {
+            // Inline schema: delegate to the schema handler.
+            let schema = schema_ref.subcomponent(schema);
+            get_effective_nullable_for_schema(&schema)
+        }
+    }
+}
+
+/// Compute effective nullability for a resolved Schema.
+///
+/// Handles recursion through single-element wrappers.
+fn get_effective_nullable_for_schema(
+    schema: &Contextual<'_, &Schema>,
+) -> anyhow::Result<EffectiveNullability> {
+    // Check for the single-element wrapper pattern.
+    let inner = match &schema.schema_kind {
+        openapiv3::SchemaKind::AllOf { all_of } if all_of.len() == 1 => {
+            Some(all_of.first().expect("checked length is 1"))
+        }
+        openapiv3::SchemaKind::AnyOf { any_of } if any_of.len() == 1 => {
+            Some(any_of.first().expect("checked length is 1"))
+        }
+        openapiv3::SchemaKind::OneOf { one_of } if one_of.len() == 1 => {
+            Some(one_of.first().expect("checked length is 1"))
+        }
+        _ => {
+            // This is either a multi-element wrapper or a non-wrapper schema.
+            // We do not handle the former case in too much depth (we treat any
+            // kind of difference as non-identical). For a non-wrapper schema,
+            // we have nowhere to recurse to. In both cases, None is fine.
+            None
+        }
+    };
+
+    // If this schema is nullable, return immediately. This check must come
+    // before the cycle check so that nullable schemas in a cycle are detected.
+    if schema.schema_data.nullable {
+        let kind = if inner.is_some() {
+            NullabilityKind::Wrapper
+        } else {
+            NullabilityKind::Direct
+        };
+        return Ok(EffectiveNullability::Nullable(kind));
+    }
+
+    // Guard against cycles (e.g., allOf: [$ref: self]).
+    //
+    // We only reach this point if the current schema is non-nullable. We only
+    // recurse (below) for non-nullable wrappers. Therefore, every schema in a
+    // cycle path is non-nullable, and returning NotNullable is correct.
+    if schema.context().stack().contains_cycle() {
+        return Ok(EffectiveNullability::NotNullable);
+    }
+
+    // If it's a wrapper, recurse into the inner schema.
+    match inner {
+        Some(inner) => {
+            let inner_ctx = Contextual::new(schema.context().clone(), inner);
+            get_effective_nullable(&inner_ctx)
+        }
+        None => Ok(EffectiveNullability::NotNullable),
+    }
+}
+
+/// Check if schema_data has any non-default values other than nullable.
+///
+/// Nullable is a semantic property, not metadata, so it should be compared
+/// separately with proper compatibility classification.
+fn has_meaningful_non_nullable_metadata(data: &SchemaData) -> bool {
+    let SchemaData {
+        // Nullable is semantic, not metadata.
+        nullable: _,
+        read_only,
+        write_only,
+        deprecated,
+        external_docs,
+        example,
+        title,
+        description,
+        discriminator,
+        default,
+        extensions,
+    } = data;
+
+    *read_only
+        || *write_only
+        || *deprecated
+        || external_docs.is_some()
+        || example.is_some()
+        || title.is_some()
+        || description.is_some()
+        || discriminator.is_some()
+        || default.is_some()
+        || !extensions.is_empty()
+}
+
+/// Check if two schema_data values differ in any field other than nullable.
+fn has_non_nullable_metadata_diff(old: &SchemaData, new: &SchemaData) -> bool {
+    let SchemaData {
+        // Nullable is semantic, not metadata.
+        nullable: _,
+        read_only: old_read_only,
+        write_only: old_write_only,
+        deprecated: old_deprecated,
+        external_docs: old_external_docs,
+        example: old_example,
+        title: old_title,
+        description: old_description,
+        discriminator: old_discriminator,
+        default: old_default,
+        extensions: old_extensions,
+    } = old;
+
+    let SchemaData {
+        nullable: _,
+        read_only: new_read_only,
+        write_only: new_write_only,
+        deprecated: new_deprecated,
+        external_docs: new_external_docs,
+        example: new_example,
+        title: new_title,
+        description: new_description,
+        discriminator: new_discriminator,
+        default: new_default,
+        extensions: new_extensions,
+    } = new;
+
+    old_read_only != new_read_only
+        || old_write_only != new_write_only
+        || old_deprecated != new_deprecated
+        || old_external_docs != new_external_docs
+        || old_example != new_example
+        || old_title != new_title
+        || old_description != new_description
+        || old_discriminator != new_discriminator
+        || old_default != new_default
+        || old_extensions != new_extensions
 }
diff --git a/tests/cases/simple/base.json b/tests/cases/simple/base.json
index 9b0c33a..9579752 100644
--- a/tests/cases/simple/base.json
+++ b/tests/cases/simple/base.json
@@ -26,6 +26,16 @@
             },
             "description": "Language for the greeting",
             "required": false
+          },
+          {
+            "name": "format",
+            "in": "query",
+            "schema": {
+              "type": "string",
+              "nullable": true
+            },
+            "description": "Output format (nullable for testing)",
+            "required": false
           }
         ],
         "responses": {
@@ -307,6 +317,116 @@
           }
         }
       }
+    },
+    "/shared": {
+      "post": {
+        "operationId": "use_shared",
+        "summary": "Uses SharedType in both request and response",
+        "requestBody": {
+          "required": true,
+          "content": {
+            "application/json": {
+              "schema": {
+                "$ref": "#/components/schemas/SharedType"
+              }
+            }
+          }
+        },
+        "responses": {
+          "200": {
+            "description": "Success",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "$ref": "#/components/schemas/SharedType"
+                }
+              }
+            }
+          }
+        }
+      }
+    },
+    "/nested-wrapper": {
+      "get": {
+        "operationId": "get_nested_wrapper",
+        "summary": "Get nested wrapper via inline allOf (tests nullable through ref chain)",
+        "responses": {
+          "200": {
+            "description": "Success",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "description": "Inline wrapper around nested chain.",
+                  "allOf": [
+                    {
+                      "$ref": "#/components/schemas/NestedWrapperA"
+                    }
+                  ]
+                }
+              }
+            }
+          }
+        }
+      }
+    },
+    "/nested-wrapper-bare-ref": {
+      "get": {
+        "operationId": "get_nested_wrapper_bare_ref",
+        "summary": "Get nested wrapper via bare ref (tests nullable through ref chain)",
+        "responses": {
+          "200": {
+            "description": "Success",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "$ref": "#/components/schemas/NestedWrapperA"
+                }
+              }
+            }
+          }
+        }
+      }
+    },
+    "/nested-nullable-wrapper": {
+      "get": {
+        "operationId": "get_nested_nullable_wrapper",
+        "summary": "Get nested nullable wrapper via inline allOf (tests nullable removal through ref chain)",
+        "responses": {
+          "200": {
+            "description": "Success",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "description": "Inline wrapper around nullable nested chain.",
+                  "allOf": [
+                    {
+                      "$ref": "#/components/schemas/NestedNullableWrapperA"
+                    }
+                  ]
+                }
+              }
+            }
+          }
+        }
+      }
+    },
+    "/nested-nullable-wrapper-bare-ref": {
+      "get": {
+        "operationId": "get_nested_nullable_wrapper_bare_ref",
+        "summary": "Get nested nullable wrapper via bare ref (tests nullable removal through ref chain)",
+        "responses": {
+          "200": {
+            "description": "Success",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "$ref": "#/components/schemas/NestedNullableWrapperA"
+                }
+              }
+            }
+          }
+        }
+      }
     }
   },
   "components": {
@@ -331,6 +451,7 @@
           },
           "via_anyof": {
             "description": "Via anyOf.",
+            "nullable": true,
             "anyOf": [
               {
                 "$ref": "#/components/schemas/SubType"
@@ -345,10 +466,35 @@
               }
             ]
           },
+          "redundant_nullable_wrapper": {
+            "description": "Nullable wrapper around already-nullable type.",
+            "nullable": true,
+            "allOf": [
+              {
+                "$ref": "#/components/schemas/NullableSubType"
+              }
+            ]
+          },
+          "nullable_via_ref": {
+            "$ref": "#/components/schemas/NullableSubType"
+          },
+          "non_nullable_wrapper_of_nullable": {
+            "description": "Non-nullable wrapper around nullable type.",
+            "allOf": [
+              {
+                "$ref": "#/components/schemas/NullableSubType"
+              }
+            ]
+          },
           "not_a_number": {
             "not": {
               "type": "number"
             }
+          },
+          "optional_field": {
+            "type": "string",
+            "description": "An optional nullable field",
+            "nullable": true
           }
         },
         "required": [
@@ -363,8 +509,18 @@
           }
         }
       },
+      "NullableSubType": {
+        "type": "object",
+        "nullable": true,
+        "properties": {
+          "value": {
+            "type": "string"
+          }
+        }
+      },
       "Tree": {
         "type": "object",
+        "nullable": true,
         "properties": {
           "children": {
             "type": "array",
@@ -379,12 +535,32 @@
         "properties": {
           "name": {
             "type": "string"
+          },
+          "description": {
+            "type": "string",
+            "nullable": true
+          },
+          "metadata_ref": {
+            "allOf": [
+              {
+                "$ref": "#/components/schemas/SubType"
+              }
+            ]
+          },
+          "metadata_nullable": {
+            "nullable": true,
+            "anyOf": [
+              {
+                "$ref": "#/components/schemas/SubType"
+              }
+            ]
           }
         },
         "required": ["name"]
       },
       "UpdateItem": {
         "type": "object",
+        "nullable": true,
         "properties": {
           "name": {
             "type": "string"
@@ -479,6 +655,71 @@
       },
       "RefChainB": {
         "$ref": "#/components/schemas/SubType"
+      },
+      "SharedType": {
+        "type": "object",
+        "properties": {
+          "id": {
+            "type": "string"
+          },
+          "data": {
+            "type": "string"
+          },
+          "optional_data": {
+            "type": "string",
+            "nullable": true
+          }
+        },
+        "required": ["id"]
+      },
+      "NestedWrapperA": {
+        "description": "Outer wrapper (non-nullable).",
+        "allOf": [
+          {
+            "$ref": "#/components/schemas/NestedWrapperB"
+          }
+        ]
+      },
+      "NestedWrapperB": {
+        "description": "Middle wrapper (non-nullable).",
+        "allOf": [
+          {
+            "$ref": "#/components/schemas/NestedWrapperC"
+          }
+        ]
+      },
+      "NestedWrapperC": {
+        "type": "object",
+        "properties": {
+          "value": {
+            "type": "string"
+          }
+        }
+      },
+      "NestedNullableWrapperA": {
+        "description": "Outer wrapper for nullable chain.",
+        "allOf": [
+          {
+            "$ref": "#/components/schemas/NestedNullableWrapperB"
+          }
+        ]
+      },
+      "NestedNullableWrapperB": {
+        "description": "Middle wrapper for nullable chain.",
+        "allOf": [
+          {
+            "$ref": "#/components/schemas/NestedNullableWrapperC"
+          }
+        ]
+      },
+      "NestedNullableWrapperC": {
+        "type": "object",
+        "nullable": true,
+        "properties": {
+          "value": {
+            "type": "string"
+          }
+        }
       }
     }
   }
diff --git a/tests/cases/simple/output/add-cookie-parameter.out b/tests/cases/simple/output/add-cookie-parameter.out
index 805b882..9221d21 100644
--- a/tests/cases/simple/output/add-cookie-parameter.out
+++ b/tests/cases/simple/output/add-cookie-parameter.out
@@ -1,6 +1,6 @@
 --- add-cookie-parameter.json
 +++ patched
-@@ -365,6 +365,16 @@
+@@ -580,6 +580,16 @@
        "get": {
          "description": "A simple ping endpoint that does nothing.",
          "operationId": "ping",
diff --git a/tests/cases/simple/output/add-default-response.out b/tests/cases/simple/output/add-default-response.out
index 712492a..22734d2 100644
--- a/tests/cases/simple/output/add-default-response.out
+++ b/tests/cases/simple/output/add-default-response.out
@@ -1,6 +1,6 @@
 --- add-default-response.json
 +++ patched
-@@ -368,6 +368,16 @@
+@@ -583,6 +583,16 @@
          "responses": {
            "200": {
              "description": "Ping successful"
diff --git a/tests/cases/simple/output/add-header-parameter.out b/tests/cases/simple/output/add-header-parameter.out
index 006a63b..c990f6c 100644
--- a/tests/cases/simple/output/add-header-parameter.out
+++ b/tests/cases/simple/output/add-header-parameter.out
@@ -1,6 +1,6 @@
 --- add-header-parameter.json
 +++ patched
-@@ -365,6 +365,16 @@
+@@ -580,6 +580,16 @@
        "get": {
          "description": "A simple ping endpoint that does nothing.",
          "operationId": "ping",
diff --git a/tests/cases/simple/output/add-operation-with-id.out b/tests/cases/simple/output/add-operation-with-id.out
index 7b51342..78a263a 100644
--- a/tests/cases/simple/output/add-operation-with-id.out
+++ b/tests/cases/simple/output/add-operation-with-id.out
@@ -1,7 +1,7 @@
 --- add-operation-with-id.json
 +++ patched
-@@ -314,6 +314,17 @@
-         "summary": "Update an item"
+@@ -529,6 +529,17 @@
+         "summary": "Get nested wrapper via bare ref (tests nullable through ref chain)"
        }
      },
 +    "/new-endpoint": {
diff --git a/tests/cases/simple/output/add-operation.out b/tests/cases/simple/output/add-operation.out
index f938e86..b6a3103 100644
--- a/tests/cases/simple/output/add-operation.out
+++ b/tests/cases/simple/output/add-operation.out
@@ -1,6 +1,6 @@
 --- add-operation.json
 +++ patched
-@@ -238,6 +238,16 @@
+@@ -361,6 +361,16 @@
          "summary": "Get arrays"
        }
      },
diff --git a/tests/cases/simple/output/add-optional-body.out b/tests/cases/simple/output/add-optional-body.out
index 75fe676..d18ce08 100644
--- a/tests/cases/simple/output/add-optional-body.out
+++ b/tests/cases/simple/output/add-optional-body.out
@@ -1,6 +1,6 @@
 --- add-optional-body.json
 +++ patched
-@@ -317,6 +317,21 @@
+@@ -532,6 +532,21 @@
      "/no-body": {
        "post": {
          "operationId": "no_body",
diff --git a/tests/cases/simple/output/add-optional-parameter.out b/tests/cases/simple/output/add-optional-parameter.out
index 34b0217..96213d9 100644
--- a/tests/cases/simple/output/add-optional-parameter.out
+++ b/tests/cases/simple/output/add-optional-parameter.out
@@ -1,7 +1,7 @@
 --- add-optional-parameter.json
 +++ patched
-@@ -257,6 +257,15 @@
-             "schema": {
+@@ -390,6 +390,15 @@
+               "nullable": true,
                "type": "string"
              }
 +          },
@@ -26,7 +26,7 @@ Result for patch:
             "#/paths/~1hello~1{name}/get",
         ],
         new_path: [
-            "#/paths/~1hello~1{name}/get/parameters/2",
+            "#/paths/~1hello~1{name}/get/parameters/3",
         ],
         comparison: Input,
         class: ForwardIncompatible,
diff --git a/tests/cases/simple/output/add-required-body.out b/tests/cases/simple/output/add-required-body.out
index 47d7d4e..4e623a9 100644
--- a/tests/cases/simple/output/add-required-body.out
+++ b/tests/cases/simple/output/add-required-body.out
@@ -1,6 +1,6 @@
 --- add-required-body.json
 +++ patched
-@@ -317,6 +317,21 @@
+@@ -532,6 +532,21 @@
      "/no-body": {
        "post": {
          "operationId": "no_body",
diff --git a/tests/cases/simple/output/add-required-parameter.out b/tests/cases/simple/output/add-required-parameter.out
index b2e82b0..45dcb34 100644
--- a/tests/cases/simple/output/add-required-parameter.out
+++ b/tests/cases/simple/output/add-required-parameter.out
@@ -1,7 +1,7 @@
 --- add-required-parameter.json
 +++ patched
-@@ -257,6 +257,15 @@
-             "schema": {
+@@ -390,6 +390,15 @@
+               "nullable": true,
                "type": "string"
              }
 +          },
@@ -21,15 +21,27 @@
 Result for patch:
 [
     Change {
-        message: "A new, required parameter 'format' was added",
+        message: "The parameter 'format' was optional and is now required",
         old_path: [
-            "#/paths/~1hello~1{name}/get",
+            "#/paths/~1hello~1{name}/get/parameters/2",
         ],
         new_path: [
-            "#/paths/~1hello~1{name}/get/parameters/2",
+            "#/paths/~1hello~1{name}/get/parameters/3",
+        ],
+        comparison: Input,
+        class: BackwardIncompatible,
+        details: MoreStrict,
+    },
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/paths/~1hello~1{name}/get/parameters/2/schema",
+        ],
+        new_path: [
+            "#/paths/~1hello~1{name}/get/parameters/3/schema",
         ],
         comparison: Input,
         class: BackwardIncompatible,
-        details: AddedRequired,
+        details: MoreStrict,
     },
 ]
diff --git a/tests/cases/simple/output/add-response-code.out b/tests/cases/simple/output/add-response-code.out
index 4d98490..b70cfb1 100644
--- a/tests/cases/simple/output/add-response-code.out
+++ b/tests/cases/simple/output/add-response-code.out
@@ -1,6 +1,6 @@
 --- add-response-code.json
 +++ patched
-@@ -368,6 +368,9 @@
+@@ -583,6 +583,9 @@
          "responses": {
            "200": {
              "description": "Ping successful"
diff --git a/tests/cases/simple/output/add-type-extension.out b/tests/cases/simple/output/add-type-extension.out
index 2b9722c..10c4388 100644
--- a/tests/cases/simple/output/add-type-extension.out
+++ b/tests/cases/simple/output/add-type-extension.out
@@ -1,6 +1,6 @@
 --- add-type-extension.json
 +++ patched
-@@ -88,7 +88,10 @@
+@@ -133,7 +133,10 @@
          "required": [
            "message"
          ],
diff --git a/tests/cases/simple/output/additional-props-non-nullable-to-nullable.out b/tests/cases/simple/output/additional-props-non-nullable-to-nullable.out
new file mode 100644
index 0000000..18b2067
--- /dev/null
+++ b/tests/cases/simple/output/additional-props-non-nullable-to-nullable.out
@@ -0,0 +1,29 @@
+--- additional-props-non-nullable-to-nullable.json
++++ patched
+@@ -225,6 +225,7 @@
+       },
+       "ObjectWithConstraints": {
+         "additionalProperties": {
++          "nullable": true,
+           "type": "string"
+         },
+         "maxProperties": 5,
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/components/schemas/ObjectWithConstraints/additionalProperties",
+            "#/paths/~1objects/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/ObjectWithConstraints/additionalProperties",
+            "#/paths/~1objects/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/allof-to-anyof.out b/tests/cases/simple/output/allof-to-anyof.out
index c65c7a9..52ee699 100644
--- a/tests/cases/simple/output/allof-to-anyof.out
+++ b/tests/cases/simple/output/allof-to-anyof.out
@@ -1,7 +1,7 @@
 --- allof-to-anyof.json
 +++ patched
-@@ -58,12 +58,12 @@
-             }
+@@ -102,12 +102,12 @@
+             "nullable": true
            },
            "via_allof": {
 -            "allOf": [
diff --git a/tests/cases/simple/output/allof-to-oneof-with-type-change.out b/tests/cases/simple/output/allof-to-oneof-with-type-change.out
index 2712e0a..dc2daab 100644
--- a/tests/cases/simple/output/allof-to-oneof-with-type-change.out
+++ b/tests/cases/simple/output/allof-to-oneof-with-type-change.out
@@ -1,7 +1,7 @@
 --- allof-to-oneof-with-type-change.json
 +++ patched
-@@ -58,12 +58,12 @@
-             }
+@@ -102,12 +102,12 @@
+             "nullable": true
            },
            "via_allof": {
 -            "allOf": [
@@ -16,7 +16,7 @@
            },
            "via_anyof": {
              "anyOf": [
-@@ -137,7 +137,7 @@
+@@ -258,7 +258,7 @@
        "SubType": {
          "properties": {
            "value": {
@@ -59,4 +59,20 @@ Result for patch:
         class: Incompatible,
         details: UnknownDifference,
     },
+    Change {
+        message: "schema types changed",
+        old_path: [
+            "#/components/schemas/SubType/properties/value",
+            "#/components/schemas/CreateItem/properties/metadata_nullable/0/$ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/SubType/properties/value",
+            "#/components/schemas/CreateItem/properties/metadata_nullable/0/$ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: Incompatible,
+        details: UnknownDifference,
+    },
 ]
diff --git a/tests/cases/simple/output/allof-to-oneof.out b/tests/cases/simple/output/allof-to-oneof.out
index 14f9d00..cd6edad 100644
--- a/tests/cases/simple/output/allof-to-oneof.out
+++ b/tests/cases/simple/output/allof-to-oneof.out
@@ -1,7 +1,7 @@
 --- allof-to-oneof.json
 +++ patched
-@@ -58,12 +58,12 @@
-             }
+@@ -102,12 +102,12 @@
+             "nullable": true
            },
            "via_allof": {
 -            "allOf": [
diff --git a/tests/cases/simple/output/allof-to-ref-with-type-change.out b/tests/cases/simple/output/allof-to-ref-with-type-change.out
index f4d9b89..1ff13e7 100644
--- a/tests/cases/simple/output/allof-to-ref-with-type-change.out
+++ b/tests/cases/simple/output/allof-to-ref-with-type-change.out
@@ -1,7 +1,7 @@
 --- allof-to-ref-with-type-change.json
 +++ patched
-@@ -58,12 +58,7 @@
-             }
+@@ -102,12 +102,7 @@
+             "nullable": true
            },
            "via_allof": {
 -            "allOf": [
@@ -14,7 +14,7 @@
            },
            "via_anyof": {
              "anyOf": [
-@@ -136,6 +131,9 @@
+@@ -257,6 +252,9 @@
        },
        "SubType": {
          "properties": {
@@ -58,4 +58,20 @@ Result for patch:
         class: Unhandled,
         details: UnknownDifference,
     },
+    Change {
+        message: "object properties changed",
+        old_path: [
+            "#/components/schemas/SubType",
+            "#/components/schemas/CreateItem/properties/metadata_nullable/0/$ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/SubType",
+            "#/components/schemas/CreateItem/properties/metadata_nullable/0/$ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: Unhandled,
+        details: UnknownDifference,
+    },
 ]
diff --git a/tests/cases/simple/output/allof-to-ref.out b/tests/cases/simple/output/allof-to-ref.out
index 7f3de13..1f87971 100644
--- a/tests/cases/simple/output/allof-to-ref.out
+++ b/tests/cases/simple/output/allof-to-ref.out
@@ -1,7 +1,7 @@
 --- allof-to-ref.json
 +++ patched
-@@ -58,12 +58,7 @@
-             }
+@@ -102,12 +102,7 @@
+             "nullable": true
            },
            "via_allof": {
 -            "allOf": [
diff --git a/tests/cases/simple/output/any-schema-change.out b/tests/cases/simple/output/any-schema-change.out
index 35a3e91..1af1eb7 100644
--- a/tests/cases/simple/output/any-schema-change.out
+++ b/tests/cases/simple/output/any-schema-change.out
@@ -1,6 +1,6 @@
 --- any-schema-change.json
 +++ patched
-@@ -48,6 +48,7 @@
+@@ -67,6 +67,7 @@
        },
        "GreetingResponse": {
          "properties": {
diff --git a/tests/cases/simple/output/anyof-to-allof.out b/tests/cases/simple/output/anyof-to-allof.out
index ced8976..ef16749 100644
--- a/tests/cases/simple/output/anyof-to-allof.out
+++ b/tests/cases/simple/output/anyof-to-allof.out
@@ -1,6 +1,6 @@
 --- anyof-to-allof.json
 +++ patched
-@@ -66,12 +66,12 @@
+@@ -110,13 +110,12 @@
              "description": "Via allOf."
            },
            "via_anyof": {
@@ -10,7 +10,8 @@
                  "$ref": "#/components/schemas/SubType"
                }
              ],
--            "description": "Via anyOf."
+-            "description": "Via anyOf.",
+-            "nullable": true
 +            "description": "Via allOf."
            },
            "via_oneof": {
@@ -19,6 +20,20 @@
 
 Result for patch:
 [
+    Change {
+        message: "nullable removed from wrapper",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
     Change {
         message: "schema metadata changed",
         old_path: [
diff --git a/tests/cases/simple/output/anyof-to-oneof.out b/tests/cases/simple/output/anyof-to-oneof.out
index 0e1f38d..0067ce6 100644
--- a/tests/cases/simple/output/anyof-to-oneof.out
+++ b/tests/cases/simple/output/anyof-to-oneof.out
@@ -1,6 +1,6 @@
 --- anyof-to-oneof.json
 +++ patched
-@@ -66,12 +66,12 @@
+@@ -110,13 +110,12 @@
              "description": "Via allOf."
            },
            "via_anyof": {
@@ -11,7 +11,8 @@
                  "$ref": "#/components/schemas/SubType"
                }
 -            ],
--            "description": "Via anyOf."
+-            "description": "Via anyOf.",
+-            "nullable": true
 +            ]
            },
            "via_oneof": {
@@ -20,6 +21,20 @@
 
 Result for patch:
 [
+    Change {
+        message: "nullable removed from wrapper",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
     Change {
         message: "schema metadata changed",
         old_path: [
diff --git a/tests/cases/simple/output/anyof-to-ref.out b/tests/cases/simple/output/anyof-to-ref.out
index 2e1d099..848cb6d 100644
--- a/tests/cases/simple/output/anyof-to-ref.out
+++ b/tests/cases/simple/output/anyof-to-ref.out
@@ -1,6 +1,6 @@
 --- anyof-to-ref.json
 +++ patched
-@@ -66,12 +66,7 @@
+@@ -110,13 +110,7 @@
              "description": "Via allOf."
            },
            "via_anyof": {
@@ -9,7 +9,8 @@
 -                "$ref": "#/components/schemas/SubType"
 -              }
 -            ],
--            "description": "Via anyOf."
+-            "description": "Via anyOf.",
+-            "nullable": true
 +            "$ref": "#/components/schemas/SubType"
            },
            "via_oneof": {
@@ -18,6 +19,20 @@
 
 Result for patch:
 [
+    Change {
+        message: "nullable removed from wrapper",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
     Change {
         message: "schema metadata removed",
         old_path: [
diff --git a/tests/cases/simple/output/array-items-non-nullable-to-nullable.out b/tests/cases/simple/output/array-items-non-nullable-to-nullable.out
new file mode 100644
index 0000000..f3a45fa
--- /dev/null
+++ b/tests/cases/simple/output/array-items-non-nullable-to-nullable.out
@@ -0,0 +1,29 @@
+--- array-items-non-nullable-to-nullable.json
++++ patched
+@@ -13,6 +13,7 @@
+       },
+       "ArrayWithConstraints": {
+         "items": {
++          "nullable": true,
+           "type": "string"
+         },
+         "maxItems": 10,
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/components/schemas/ArrayWithConstraints/items",
+            "#/paths/~1arrays/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/ArrayWithConstraints/items",
+            "#/paths/~1arrays/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/array-items-remove.out b/tests/cases/simple/output/array-items-remove.out
index 426e982..097a94c 100644
--- a/tests/cases/simple/output/array-items-remove.out
+++ b/tests/cases/simple/output/array-items-remove.out
@@ -1,10 +1,11 @@
 --- array-items-remove.json
 +++ patched
-@@ -146,7 +146,7 @@
+@@ -268,7 +268,8 @@
          "properties": {
            "children": {
              "items": {
 -              "$ref": "#/components/schemas/Tree"
++              "nullable": true,
 +              "type": "string"
              },
              "type": "array"
diff --git a/tests/cases/simple/output/body-description-change.out b/tests/cases/simple/output/body-description-change.out
index 3e2eb01..cdd8d9c 100644
--- a/tests/cases/simple/output/body-description-change.out
+++ b/tests/cases/simple/output/body-description-change.out
@@ -1,6 +1,6 @@
 --- body-description-change.json
 +++ patched
-@@ -285,6 +285,7 @@
+@@ -418,6 +418,7 @@
                }
              }
            },
diff --git a/tests/cases/simple/output/body-extension-change.out b/tests/cases/simple/output/body-extension-change.out
index 06cbc81..427c709 100644
--- a/tests/cases/simple/output/body-extension-change.out
+++ b/tests/cases/simple/output/body-extension-change.out
@@ -1,6 +1,6 @@
 --- body-extension-change.json
 +++ patched
-@@ -285,7 +285,8 @@
+@@ -418,7 +418,8 @@
                }
              }
            },
diff --git a/tests/cases/simple/output/body-optional-to-required.out b/tests/cases/simple/output/body-optional-to-required.out
index b09a68f..881e6e8 100644
--- a/tests/cases/simple/output/body-optional-to-required.out
+++ b/tests/cases/simple/output/body-optional-to-required.out
@@ -1,6 +1,6 @@
 --- body-optional-to-required.json
 +++ patched
-@@ -304,7 +304,7 @@
+@@ -437,7 +437,7 @@
                }
              }
            },
diff --git a/tests/cases/simple/output/body-required-to-optional.out b/tests/cases/simple/output/body-required-to-optional.out
index a41b06d..fabd1bc 100644
--- a/tests/cases/simple/output/body-required-to-optional.out
+++ b/tests/cases/simple/output/body-required-to-optional.out
@@ -1,6 +1,6 @@
 --- body-required-to-optional.json
 +++ patched
-@@ -285,7 +285,7 @@
+@@ -418,7 +418,7 @@
                }
              }
            },
diff --git a/tests/cases/simple/output/boolean-change.out b/tests/cases/simple/output/boolean-change.out
index 6fc74f3..3a7dd5e 100644
--- a/tests/cases/simple/output/boolean-change.out
+++ b/tests/cases/simple/output/boolean-change.out
@@ -1,6 +1,6 @@
 --- boolean-change.json
 +++ patched
-@@ -159,6 +159,7 @@
+@@ -281,6 +281,7 @@
              "type": "integer"
            },
            "enabled": {
diff --git a/tests/cases/simple/output/boolean-enum-change.out b/tests/cases/simple/output/boolean-enum-change.out
index 670c172..154f21a 100644
--- a/tests/cases/simple/output/boolean-enum-change.out
+++ b/tests/cases/simple/output/boolean-enum-change.out
@@ -1,6 +1,6 @@
 --- boolean-enum-change.json
 +++ patched
-@@ -159,6 +159,9 @@
+@@ -281,6 +281,9 @@
              "type": "integer"
            },
            "enabled": {
diff --git a/tests/cases/simple/output/change-default-response.out b/tests/cases/simple/output/change-default-response.out
index 51a21da..04583bc 100644
--- a/tests/cases/simple/output/change-default-response.out
+++ b/tests/cases/simple/output/change-default-response.out
@@ -1,6 +1,6 @@
 --- change-default-response.json
 +++ patched
-@@ -451,7 +451,7 @@
+@@ -694,7 +694,7 @@
                  }
                }
              },
diff --git a/tests/cases/simple/output/change-header-parameter.out b/tests/cases/simple/output/change-header-parameter.out
index 8b8fec2..41dcaa9 100644
--- a/tests/cases/simple/output/change-header-parameter.out
+++ b/tests/cases/simple/output/change-header-parameter.out
@@ -1,6 +1,6 @@
 --- change-header-parameter.json
 +++ patched
-@@ -466,7 +466,7 @@
+@@ -709,7 +709,7 @@
              "name": "X-Request-Id",
              "required": true,
              "schema": {
diff --git a/tests/cases/simple/output/change-operation-parameter-requirement.out b/tests/cases/simple/output/change-operation-parameter-requirement.out
index dccb0ce..1739f62 100644
--- a/tests/cases/simple/output/change-operation-parameter-requirement.out
+++ b/tests/cases/simple/output/change-operation-parameter-requirement.out
@@ -1,6 +1,6 @@
 --- change-operation-parameter-requirement.json
 +++ patched
-@@ -253,7 +253,7 @@
+@@ -376,7 +376,7 @@
              "description": "Language for the greeting",
              "in": "query",
              "name": "language",
diff --git a/tests/cases/simple/output/change-operation-parameter-type.out b/tests/cases/simple/output/change-operation-parameter-type.out
index 1a21afd..cd8f68b 100644
--- a/tests/cases/simple/output/change-operation-parameter-type.out
+++ b/tests/cases/simple/output/change-operation-parameter-type.out
@@ -1,14 +1,14 @@
 --- change-operation-parameter-type.json
 +++ patched
-@@ -255,7 +255,7 @@
+@@ -378,7 +378,7 @@
              "name": "language",
              "required": false,
              "schema": {
 -              "type": "string"
 +              "type": "integer"
              }
-           }
-         ],
+           },
+           {
 
 
 Result for patch:
diff --git a/tests/cases/simple/output/change-property-type.out b/tests/cases/simple/output/change-property-type.out
index 59b6235..206167b 100644
--- a/tests/cases/simple/output/change-property-type.out
+++ b/tests/cases/simple/output/change-property-type.out
@@ -1,14 +1,14 @@
 --- change-property-type.json
 +++ patched
-@@ -50,7 +50,7 @@
+@@ -69,7 +69,7 @@
          "properties": {
            "message": {
              "description": "The greeting message",
 -            "type": "string"
 +            "type": "integer"
            },
-           "not_a_number": {
-             "not": {
+           "non_nullable_wrapper_of_nullable": {
+             "allOf": [
 
 
 Result for patch:
diff --git a/tests/cases/simple/output/inline-to-allof.out b/tests/cases/simple/output/inline-to-allof.out
index 5173ba2..dfdf9b2 100644
--- a/tests/cases/simple/output/inline-to-allof.out
+++ b/tests/cases/simple/output/inline-to-allof.out
@@ -1,6 +1,6 @@
 --- inline-to-allof.json
 +++ patched
-@@ -246,7 +246,12 @@
+@@ -369,7 +369,12 @@
              "in": "path",
              "name": "name",
              "schema": {
diff --git a/tests/cases/simple/output/inline-to-wrapper-nullable-added.out b/tests/cases/simple/output/inline-to-wrapper-nullable-added.out
new file mode 100644
index 0000000..83c2e2e
--- /dev/null
+++ b/tests/cases/simple/output/inline-to-wrapper-nullable-added.out
@@ -0,0 +1,64 @@
+--- inline-to-wrapper-nullable-added.json
++++ patched
+@@ -68,8 +68,13 @@
+       "GreetingResponse": {
+         "properties": {
+           "message": {
++            "allOf": [
++              {
++                "type": "string"
++              }
++            ],
+             "description": "The greeting message",
+-            "type": "string"
++            "nullable": true
+           },
+           "non_nullable_wrapper_of_nullable": {
+             "allOf": [
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable added at wrapper",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/message",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/message",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+    Change {
+        message: "schema metadata added",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/message",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/message",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: Trivial,
+        details: Metadata,
+    },
+    Change {
+        message: "schema metadata changed",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/message",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/message/0",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: Trivial,
+        details: Metadata,
+    },
+]
diff --git a/tests/cases/simple/output/input-non-nullable-to-nullable.out b/tests/cases/simple/output/input-non-nullable-to-nullable.out
new file mode 100644
index 0000000..8321e87
--- /dev/null
+++ b/tests/cases/simple/output/input-non-nullable-to-nullable.out
@@ -0,0 +1,29 @@
+--- input-non-nullable-to-nullable.json
++++ patched
+@@ -42,6 +42,7 @@
+             ]
+           },
+           "name": {
++            "nullable": true,
+             "type": "string"
+           }
+         },
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/components/schemas/CreateItem/properties/name",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/CreateItem/properties/name",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: ForwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/input-nullable-to-non-nullable.out b/tests/cases/simple/output/input-nullable-to-non-nullable.out
new file mode 100644
index 0000000..8a640fd
--- /dev/null
+++ b/tests/cases/simple/output/input-nullable-to-non-nullable.out
@@ -0,0 +1,29 @@
+--- input-nullable-to-non-nullable.json
++++ patched
+@@ -23,7 +23,6 @@
+       "CreateItem": {
+         "properties": {
+           "description": {
+-            "nullable": true,
+             "type": "string"
+           },
+           "metadata_nullable": {
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/components/schemas/CreateItem/properties/description",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/CreateItem/properties/description",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: BackwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/input-ref-to-wrapper-nullable-added.out b/tests/cases/simple/output/input-ref-to-wrapper-nullable-added.out
new file mode 100644
index 0000000..a8ad526
--- /dev/null
+++ b/tests/cases/simple/output/input-ref-to-wrapper-nullable-added.out
@@ -0,0 +1,35 @@
+--- input-ref-to-wrapper-nullable-added.json
++++ patched
+@@ -42,7 +42,12 @@
+             ]
+           },
+           "name": {
+-            "type": "string"
++            "allOf": [
++              {
++                "type": "string"
++              }
++            ],
++            "nullable": true
+           }
+         },
+         "required": [
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable added at wrapper",
+        old_path: [
+            "#/components/schemas/CreateItem/properties/name",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/CreateItem/properties/name",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: ForwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/input-root-non-nullable-to-nullable.out b/tests/cases/simple/output/input-root-non-nullable-to-nullable.out
new file mode 100644
index 0000000..950b475
--- /dev/null
+++ b/tests/cases/simple/output/input-root-non-nullable-to-nullable.out
@@ -0,0 +1,27 @@
+--- input-root-non-nullable-to-nullable.json
++++ patched
+@@ -21,6 +21,7 @@
+         "uniqueItems": false
+       },
+       "CreateItem": {
++        "nullable": true,
+         "properties": {
+           "description": {
+             "nullable": true,
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/paths/~1items/post/request_body/content/application~1json/schema",
+        ],
+        new_path: [
+            "#/paths/~1items/post/request_body/content/application~1json/schema",
+        ],
+        comparison: Input,
+        class: ForwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/input-root-nullable-to-non-nullable.out b/tests/cases/simple/output/input-root-nullable-to-non-nullable.out
new file mode 100644
index 0000000..b14a91c
--- /dev/null
+++ b/tests/cases/simple/output/input-root-nullable-to-non-nullable.out
@@ -0,0 +1,27 @@
+--- input-root-nullable-to-non-nullable.json
++++ patched
+@@ -290,7 +290,6 @@
+         "type": "object"
+       },
+       "UpdateItem": {
+-        "nullable": true,
+         "properties": {
+           "name": {
+             "type": "string"
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/paths/~1items/put/request_body/content/application~1json/schema",
+        ],
+        new_path: [
+            "#/paths/~1items/put/request_body/content/application~1json/schema",
+        ],
+        comparison: Input,
+        class: BackwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/input-wrapper-non-nullable-to-nullable.out b/tests/cases/simple/output/input-wrapper-non-nullable-to-nullable.out
new file mode 100644
index 0000000..1741b62
--- /dev/null
+++ b/tests/cases/simple/output/input-wrapper-non-nullable-to-nullable.out
@@ -0,0 +1,31 @@
+--- input-wrapper-non-nullable-to-nullable.json
++++ patched
+@@ -39,7 +39,8 @@
+               {
+                 "$ref": "#/components/schemas/SubType"
+               }
+-            ]
++            ],
++            "nullable": true
+           },
+           "name": {
+             "type": "string"
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable added at wrapper",
+        old_path: [
+            "#/components/schemas/CreateItem/properties/metadata_ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/CreateItem/properties/metadata_ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: ForwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/input-wrapper-nullable-to-non-nullable.out b/tests/cases/simple/output/input-wrapper-nullable-to-non-nullable.out
new file mode 100644
index 0000000..e6b8fef
--- /dev/null
+++ b/tests/cases/simple/output/input-wrapper-nullable-to-non-nullable.out
@@ -0,0 +1,31 @@
+--- input-wrapper-nullable-to-non-nullable.json
++++ patched
+@@ -31,8 +31,7 @@
+               {
+                 "$ref": "#/components/schemas/SubType"
+               }
+-            ],
+-            "nullable": true
++            ]
+           },
+           "metadata_ref": {
+             "allOf": [
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable removed from wrapper",
+        old_path: [
+            "#/components/schemas/CreateItem/properties/metadata_nullable",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/CreateItem/properties/metadata_nullable",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: BackwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/input-wrapper-to-ref-nullable-removed.out b/tests/cases/simple/output/input-wrapper-to-ref-nullable-removed.out
new file mode 100644
index 0000000..d6631b1
--- /dev/null
+++ b/tests/cases/simple/output/input-wrapper-to-ref-nullable-removed.out
@@ -0,0 +1,35 @@
+--- input-wrapper-to-ref-nullable-removed.json
++++ patched
+@@ -27,12 +27,7 @@
+             "type": "string"
+           },
+           "metadata_nullable": {
+-            "anyOf": [
+-              {
+-                "$ref": "#/components/schemas/SubType"
+-              }
+-            ],
+-            "nullable": true
++            "$ref": "#/components/schemas/SubType"
+           },
+           "metadata_ref": {
+             "allOf": [
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable removed from wrapper",
+        old_path: [
+            "#/components/schemas/CreateItem/properties/metadata_nullable",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/CreateItem/properties/metadata_nullable",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: BackwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/integer-format-change.out b/tests/cases/simple/output/integer-format-change.out
index f97a7a4..fe5f8fc 100644
--- a/tests/cases/simple/output/integer-format-change.out
+++ b/tests/cases/simple/output/integer-format-change.out
@@ -1,6 +1,6 @@
 --- integer-format-change.json
 +++ patched
-@@ -156,6 +156,7 @@
+@@ -278,6 +278,7 @@
        "TypedProperties": {
          "properties": {
            "count": {
diff --git a/tests/cases/simple/output/modify-cycle-type.out b/tests/cases/simple/output/modify-cycle-type.out
index 4dd795b..a42b4b3 100644
--- a/tests/cases/simple/output/modify-cycle-type.out
+++ b/tests/cases/simple/output/modify-cycle-type.out
@@ -1,7 +1,7 @@
 --- modify-cycle-type.json
 +++ patched
-@@ -145,10 +145,7 @@
-       "Tree": {
+@@ -267,10 +267,7 @@
+         "nullable": true,
          "properties": {
            "children": {
 -            "items": {
@@ -16,6 +16,20 @@
 
 Result for patch:
 [
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/components/schemas/Tree/properties/children",
+            "#/paths/~1tree/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/Tree/properties/children",
+            "#/paths/~1tree/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
     Change {
         message: "schema types changed",
         old_path: [
diff --git a/tests/cases/simple/output/multi-allof-variant-change.out b/tests/cases/simple/output/multi-allof-variant-change.out
index b2c82ec..e8bf201 100644
--- a/tests/cases/simple/output/multi-allof-variant-change.out
+++ b/tests/cases/simple/output/multi-allof-variant-change.out
@@ -1,6 +1,6 @@
 --- multi-allof-variant-change.json
 +++ patched
-@@ -95,7 +95,7 @@
+@@ -140,7 +140,7 @@
            {
              "properties": {
                "id": {
diff --git a/tests/cases/simple/output/multi-oneof-count-change.out b/tests/cases/simple/output/multi-oneof-count-change.out
index 8d054d6..6189abe 100644
--- a/tests/cases/simple/output/multi-oneof-count-change.out
+++ b/tests/cases/simple/output/multi-oneof-count-change.out
@@ -1,6 +1,6 @@
 --- multi-oneof-count-change.json
 +++ patched
-@@ -117,6 +117,9 @@
+@@ -162,6 +162,9 @@
            },
            {
              "type": "integer"
diff --git a/tests/cases/simple/output/multi-oneof-variant-change.out b/tests/cases/simple/output/multi-oneof-variant-change.out
index 9e67399..2d5506b 100644
--- a/tests/cases/simple/output/multi-oneof-variant-change.out
+++ b/tests/cases/simple/output/multi-oneof-variant-change.out
@@ -1,6 +1,6 @@
 --- multi-oneof-variant-change.json
 +++ patched
-@@ -113,7 +113,7 @@
+@@ -158,7 +158,7 @@
        "MultiOneOf": {
          "oneOf": [
            {
diff --git a/tests/cases/simple/output/nested-wrapper-non-nullable-to-nullable.out b/tests/cases/simple/output/nested-wrapper-non-nullable-to-nullable.out
new file mode 100644
index 0000000..00ef186
--- /dev/null
+++ b/tests/cases/simple/output/nested-wrapper-non-nullable-to-nullable.out
@@ -0,0 +1,39 @@
+--- nested-wrapper-non-nullable-to-nullable.json
++++ patched
+@@ -207,6 +207,7 @@
+         "description": "Middle wrapper (non-nullable)."
+       },
+       "NestedWrapperC": {
++        "nullable": true,
+         "properties": {
+           "value": {
+             "type": "string"
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/paths/~1nested-wrapper/get/responses/200/content/application~1json/schema",
+        ],
+        new_path: [
+            "#/paths/~1nested-wrapper/get/responses/200/content/application~1json/schema",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/paths/~1nested-wrapper-bare-ref/get/responses/200/content/application~1json/schema",
+        ],
+        new_path: [
+            "#/paths/~1nested-wrapper-bare-ref/get/responses/200/content/application~1json/schema",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/nested-wrapper-nullable-to-non-nullable.out b/tests/cases/simple/output/nested-wrapper-nullable-to-non-nullable.out
new file mode 100644
index 0000000..d228bfd
--- /dev/null
+++ b/tests/cases/simple/output/nested-wrapper-nullable-to-non-nullable.out
@@ -0,0 +1,39 @@
+--- nested-wrapper-nullable-to-non-nullable.json
++++ patched
+@@ -182,7 +182,6 @@
+         "description": "Middle wrapper for nullable chain."
+       },
+       "NestedNullableWrapperC": {
+-        "nullable": true,
+         "properties": {
+           "value": {
+             "type": "string"
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/paths/~1nested-nullable-wrapper/get/responses/200/content/application~1json/schema",
+        ],
+        new_path: [
+            "#/paths/~1nested-nullable-wrapper/get/responses/200/content/application~1json/schema",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/paths/~1nested-nullable-wrapper-bare-ref/get/responses/200/content/application~1json/schema",
+        ],
+        new_path: [
+            "#/paths/~1nested-nullable-wrapper-bare-ref/get/responses/200/content/application~1json/schema",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/non-nullable-to-nullable.out b/tests/cases/simple/output/non-nullable-to-nullable.out
new file mode 100644
index 0000000..9f35399
--- /dev/null
+++ b/tests/cases/simple/output/non-nullable-to-nullable.out
@@ -0,0 +1,29 @@
+--- non-nullable-to-nullable.json
++++ patched
+@@ -69,6 +69,7 @@
+         "properties": {
+           "message": {
+             "description": "The greeting message",
++            "nullable": true,
+             "type": "string"
+           },
+           "non_nullable_wrapper_of_nullable": {
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/message",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/message",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/not-inner-to-allof.out b/tests/cases/simple/output/not-inner-to-allof.out
index c3c4808..8f6d42a 100644
--- a/tests/cases/simple/output/not-inner-to-allof.out
+++ b/tests/cases/simple/output/not-inner-to-allof.out
@@ -1,6 +1,6 @@
 --- not-inner-to-allof.json
 +++ patched
-@@ -54,7 +54,12 @@
+@@ -81,7 +81,12 @@
            },
            "not_a_number": {
              "not": {
@@ -13,7 +13,7 @@
 +              "description": "A number type"
              }
            },
-           "via_allof": {
+           "nullable_via_ref": {
 
 
 Result for patch:
diff --git a/tests/cases/simple/output/not-to-allof.out b/tests/cases/simple/output/not-to-allof.out
index b3ef213..07ecc11 100644
--- a/tests/cases/simple/output/not-to-allof.out
+++ b/tests/cases/simple/output/not-to-allof.out
@@ -1,7 +1,7 @@
 --- not-to-allof.json
 +++ patched
-@@ -53,9 +53,14 @@
-             "type": "string"
+@@ -80,9 +80,14 @@
+             "description": "Non-nullable wrapper around nullable type."
            },
            "not_a_number": {
 -            "not": {
@@ -16,8 +16,8 @@
 +            ],
 +            "description": "Not a number, wrapped in allOf"
            },
-           "via_allof": {
-             "allOf": [
+           "nullable_via_ref": {
+             "$ref": "#/components/schemas/NullableSubType"
 
 
 Result for patch:
diff --git a/tests/cases/simple/output/nullable-to-non-nullable.out b/tests/cases/simple/output/nullable-to-non-nullable.out
new file mode 100644
index 0000000..51ff898
--- /dev/null
+++ b/tests/cases/simple/output/nullable-to-non-nullable.out
@@ -0,0 +1,29 @@
+--- nullable-to-non-nullable.json
++++ patched
+@@ -89,7 +89,6 @@
+           },
+           "optional_field": {
+             "description": "An optional nullable field",
+-            "nullable": true,
+             "type": "string"
+           },
+           "redundant_nullable_wrapper": {
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/optional_field",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/optional_field",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/number-constraints-change.out b/tests/cases/simple/output/number-constraints-change.out
index 241849d..46579f2 100644
--- a/tests/cases/simple/output/number-constraints-change.out
+++ b/tests/cases/simple/output/number-constraints-change.out
@@ -1,6 +1,6 @@
 --- number-constraints-change.json
 +++ patched
-@@ -162,6 +162,7 @@
+@@ -284,6 +284,7 @@
              "type": "boolean"
            },
            "ratio": {
diff --git a/tests/cases/simple/output/object-additional-props-false.out b/tests/cases/simple/output/object-additional-props-false.out
index 7eb6590..c0859f1 100644
--- a/tests/cases/simple/output/object-additional-props-false.out
+++ b/tests/cases/simple/output/object-additional-props-false.out
@@ -1,7 +1,7 @@
 --- object-additional-props-false.json
 +++ patched
-@@ -121,9 +121,7 @@
-         ]
+@@ -224,9 +224,7 @@
+         "type": "object"
        },
        "ObjectWithConstraints": {
 -        "additionalProperties": {
diff --git a/tests/cases/simple/output/object-additional-props-schema-change.out b/tests/cases/simple/output/object-additional-props-schema-change.out
index e702620..e956d14 100644
--- a/tests/cases/simple/output/object-additional-props-schema-change.out
+++ b/tests/cases/simple/output/object-additional-props-schema-change.out
@@ -1,6 +1,6 @@
 --- object-additional-props-schema-change.json
 +++ patched
-@@ -122,7 +122,7 @@
+@@ -225,7 +225,7 @@
        },
        "ObjectWithConstraints": {
          "additionalProperties": {
diff --git a/tests/cases/simple/output/object-additional-props-type-change.out b/tests/cases/simple/output/object-additional-props-type-change.out
index dd355d5..91fdf65 100644
--- a/tests/cases/simple/output/object-additional-props-type-change.out
+++ b/tests/cases/simple/output/object-additional-props-type-change.out
@@ -1,7 +1,7 @@
 --- object-additional-props-type-change.json
 +++ patched
-@@ -121,9 +121,7 @@
-         ]
+@@ -224,9 +224,7 @@
+         "type": "object"
        },
        "ObjectWithConstraints": {
 -        "additionalProperties": {
diff --git a/tests/cases/simple/output/object-max-properties-change.out b/tests/cases/simple/output/object-max-properties-change.out
index c519851..f77067f 100644
--- a/tests/cases/simple/output/object-max-properties-change.out
+++ b/tests/cases/simple/output/object-max-properties-change.out
@@ -1,6 +1,6 @@
 --- object-max-properties-change.json
 +++ patched
-@@ -124,7 +124,7 @@
+@@ -227,7 +227,7 @@
          "additionalProperties": {
            "type": "string"
          },
diff --git a/tests/cases/simple/output/object-min-properties-change.out b/tests/cases/simple/output/object-min-properties-change.out
index cc5eca9..b97583f 100644
--- a/tests/cases/simple/output/object-min-properties-change.out
+++ b/tests/cases/simple/output/object-min-properties-change.out
@@ -1,6 +1,6 @@
 --- object-min-properties-change.json
 +++ patched
-@@ -125,7 +125,7 @@
+@@ -228,7 +228,7 @@
            "type": "string"
          },
          "maxProperties": 5,
diff --git a/tests/cases/simple/output/oneof-to-allof.out b/tests/cases/simple/output/oneof-to-allof.out
index 78d37b8..6e4b649 100644
--- a/tests/cases/simple/output/oneof-to-allof.out
+++ b/tests/cases/simple/output/oneof-to-allof.out
@@ -1,7 +1,7 @@
 --- oneof-to-allof.json
 +++ patched
-@@ -74,12 +74,12 @@
-             "description": "Via anyOf."
+@@ -119,12 +119,12 @@
+             "nullable": true
            },
            "via_oneof": {
 -            "description": "Via oneOf.",
diff --git a/tests/cases/simple/output/oneof-to-anyof.out b/tests/cases/simple/output/oneof-to-anyof.out
index c643d8b..89d4909 100644
--- a/tests/cases/simple/output/oneof-to-anyof.out
+++ b/tests/cases/simple/output/oneof-to-anyof.out
@@ -1,7 +1,7 @@
 --- oneof-to-anyof.json
 +++ patched
-@@ -74,12 +74,12 @@
-             "description": "Via anyOf."
+@@ -119,12 +119,12 @@
+             "nullable": true
            },
            "via_oneof": {
 -            "description": "Via oneOf.",
diff --git a/tests/cases/simple/output/oneof-to-ref.out b/tests/cases/simple/output/oneof-to-ref.out
index 0ec92a5..97ec3c3 100644
--- a/tests/cases/simple/output/oneof-to-ref.out
+++ b/tests/cases/simple/output/oneof-to-ref.out
@@ -1,7 +1,7 @@
 --- oneof-to-ref.json
 +++ patched
-@@ -74,12 +74,7 @@
-             "description": "Via anyOf."
+@@ -119,12 +119,7 @@
+             "nullable": true
            },
            "via_oneof": {
 -            "description": "Via oneOf.",
diff --git a/tests/cases/simple/output/output-root-non-nullable-to-nullable.out b/tests/cases/simple/output/output-root-non-nullable-to-nullable.out
new file mode 100644
index 0000000..5ae81d7
--- /dev/null
+++ b/tests/cases/simple/output/output-root-non-nullable-to-nullable.out
@@ -0,0 +1,27 @@
+--- output-root-non-nullable-to-nullable.json
++++ patched
+@@ -66,6 +66,7 @@
+         "type": "object"
+       },
+       "GreetingResponse": {
++        "nullable": true,
+         "properties": {
+           "message": {
+             "description": "The greeting message",
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema",
+        ],
+        new_path: [
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/output-root-nullable-to-non-nullable.out b/tests/cases/simple/output/output-root-nullable-to-non-nullable.out
new file mode 100644
index 0000000..64fa183
--- /dev/null
+++ b/tests/cases/simple/output/output-root-nullable-to-non-nullable.out
@@ -0,0 +1,41 @@
+--- output-root-nullable-to-non-nullable.json
++++ patched
+@@ -264,7 +264,6 @@
+         "type": "object"
+       },
+       "Tree": {
+-        "nullable": true,
+         "properties": {
+           "children": {
+             "items": {
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/paths/~1tree/get/responses/200/content/application~1json/schema",
+        ],
+        new_path: [
+            "#/paths/~1tree/get/responses/200/content/application~1json/schema",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/components/schemas/Tree/properties/children/items",
+            "#/paths/~1tree/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/Tree/properties/children/items",
+            "#/paths/~1tree/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/param-non-nullable-to-nullable.out b/tests/cases/simple/output/param-non-nullable-to-nullable.out
new file mode 100644
index 0000000..ab33b93
--- /dev/null
+++ b/tests/cases/simple/output/param-non-nullable-to-nullable.out
@@ -0,0 +1,27 @@
+--- param-non-nullable-to-nullable.json
++++ patched
+@@ -378,6 +378,7 @@
+             "name": "language",
+             "required": false,
+             "schema": {
++              "nullable": true,
+               "type": "string"
+             }
+           },
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/paths/~1hello~1{name}/get/parameters/1/schema",
+        ],
+        new_path: [
+            "#/paths/~1hello~1{name}/get/parameters/1/schema",
+        ],
+        comparison: Input,
+        class: ForwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/param-nullable-to-non-nullable.out b/tests/cases/simple/output/param-nullable-to-non-nullable.out
new file mode 100644
index 0000000..c1177e3
--- /dev/null
+++ b/tests/cases/simple/output/param-nullable-to-non-nullable.out
@@ -0,0 +1,27 @@
+--- param-nullable-to-non-nullable.json
++++ patched
+@@ -387,7 +387,6 @@
+             "name": "format",
+             "required": false,
+             "schema": {
+-              "nullable": true,
+               "type": "string"
+             }
+           }
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/paths/~1hello~1{name}/get/parameters/2/schema",
+        ],
+        new_path: [
+            "#/paths/~1hello~1{name}/get/parameters/2/schema",
+        ],
+        comparison: Input,
+        class: BackwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/param-required-to-optional.out b/tests/cases/simple/output/param-required-to-optional.out
index c955a3c..a79a050 100644
--- a/tests/cases/simple/output/param-required-to-optional.out
+++ b/tests/cases/simple/output/param-required-to-optional.out
@@ -1,6 +1,6 @@
 --- param-required-to-optional.json
 +++ patched
-@@ -464,7 +464,7 @@
+@@ -707,7 +707,7 @@
            {
              "in": "header",
              "name": "X-Request-Id",
diff --git a/tests/cases/simple/output/param-schema-to-content.out b/tests/cases/simple/output/param-schema-to-content.out
index b9f44c6..715122d 100644
--- a/tests/cases/simple/output/param-schema-to-content.out
+++ b/tests/cases/simple/output/param-schema-to-content.out
@@ -1,6 +1,6 @@
 --- param-schema-to-content.json
 +++ patched
-@@ -250,13 +250,17 @@
+@@ -373,13 +373,17 @@
              }
            },
            {
@@ -19,9 +19,9 @@
 -              "type": "string"
 -            }
 +            "required": false
-           }
-         ],
-         "responses": {
+           },
+           {
+             "description": "Output format (nullable for testing)",
 
 
 Result for patch:
diff --git a/tests/cases/simple/output/redundant-wrapper-nullable-added.out b/tests/cases/simple/output/redundant-wrapper-nullable-added.out
new file mode 100644
index 0000000..9bba164
--- /dev/null
+++ b/tests/cases/simple/output/redundant-wrapper-nullable-added.out
@@ -0,0 +1,16 @@
+--- redundant-wrapper-nullable-added.json
++++ patched
+@@ -77,7 +77,8 @@
+                 "$ref": "#/components/schemas/NullableSubType"
+               }
+             ],
+-            "description": "Non-nullable wrapper around nullable type."
++            "description": "Non-nullable wrapper around nullable type.",
++            "nullable": true
+           },
+           "not_a_number": {
+             "not": {
+
+
+Result for patch:
+[]
diff --git a/tests/cases/simple/output/redundant-wrapper-nullable-removed.out b/tests/cases/simple/output/redundant-wrapper-nullable-removed.out
new file mode 100644
index 0000000..90c8099
--- /dev/null
+++ b/tests/cases/simple/output/redundant-wrapper-nullable-removed.out
@@ -0,0 +1,16 @@
+--- redundant-wrapper-nullable-removed.json
++++ patched
+@@ -98,8 +98,7 @@
+                 "$ref": "#/components/schemas/NullableSubType"
+               }
+             ],
+-            "description": "Nullable wrapper around already-nullable type.",
+-            "nullable": true
++            "description": "Nullable wrapper around already-nullable type."
+           },
+           "via_allof": {
+             "allOf": [
+
+
+Result for patch:
+[]
diff --git a/tests/cases/simple/output/redundant-wrapper-to-ref.out b/tests/cases/simple/output/redundant-wrapper-to-ref.out
new file mode 100644
index 0000000..68012ad
--- /dev/null
+++ b/tests/cases/simple/output/redundant-wrapper-to-ref.out
@@ -0,0 +1,36 @@
+--- redundant-wrapper-to-ref.json
++++ patched
+@@ -93,13 +93,7 @@
+             "type": "string"
+           },
+           "redundant_nullable_wrapper": {
+-            "allOf": [
+-              {
+-                "$ref": "#/components/schemas/NullableSubType"
+-              }
+-            ],
+-            "description": "Nullable wrapper around already-nullable type.",
+-            "nullable": true
++            "$ref": "#/components/schemas/NullableSubType"
+           },
+           "via_allof": {
+             "allOf": [
+
+
+Result for patch:
+[
+    Change {
+        message: "schema metadata removed",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/redundant_nullable_wrapper",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/redundant_nullable_wrapper",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: Trivial,
+        details: Metadata,
+    },
+]
diff --git a/tests/cases/simple/output/ref-chain-change.out b/tests/cases/simple/output/ref-chain-change.out
index 9d3bca3..b561fae 100644
--- a/tests/cases/simple/output/ref-chain-change.out
+++ b/tests/cases/simple/output/ref-chain-change.out
@@ -1,13 +1,13 @@
 --- ref-chain-change.json
 +++ patched
-@@ -132,7 +132,7 @@
+@@ -235,7 +235,7 @@
          "$ref": "#/components/schemas/RefChainB"
        },
        "RefChainB": {
 -        "$ref": "#/components/schemas/SubType"
 +        "$ref": "#/components/schemas/ErrorResponse"
        },
-       "SubType": {
+       "SharedType": {
          "properties": {
 
 
diff --git a/tests/cases/simple/output/ref-to-allof.out b/tests/cases/simple/output/ref-to-allof.out
index 0ffecab..dddebb5 100644
--- a/tests/cases/simple/output/ref-to-allof.out
+++ b/tests/cases/simple/output/ref-to-allof.out
@@ -1,6 +1,6 @@
 --- ref-to-allof.json
 +++ patched
-@@ -82,7 +82,12 @@
+@@ -127,7 +127,12 @@
              ]
            },
            "via_ref": {
diff --git a/tests/cases/simple/output/ref-to-anyof.out b/tests/cases/simple/output/ref-to-anyof.out
index f764670..b2e51f0 100644
--- a/tests/cases/simple/output/ref-to-anyof.out
+++ b/tests/cases/simple/output/ref-to-anyof.out
@@ -1,6 +1,6 @@
 --- ref-to-anyof.json
 +++ patched
-@@ -82,7 +82,12 @@
+@@ -127,7 +127,12 @@
              ]
            },
            "via_ref": {
diff --git a/tests/cases/simple/output/ref-to-inline-allof.out b/tests/cases/simple/output/ref-to-inline-allof.out
index 41f89a9..625a3ab 100644
--- a/tests/cases/simple/output/ref-to-inline-allof.out
+++ b/tests/cases/simple/output/ref-to-inline-allof.out
@@ -1,6 +1,6 @@
 --- ref-to-inline-allof.json
 +++ patched
-@@ -82,7 +82,18 @@
+@@ -127,7 +127,18 @@
              ]
            },
            "via_ref": {
diff --git a/tests/cases/simple/output/ref-to-oneof.out b/tests/cases/simple/output/ref-to-oneof.out
index 4f95563..ef12459 100644
--- a/tests/cases/simple/output/ref-to-oneof.out
+++ b/tests/cases/simple/output/ref-to-oneof.out
@@ -1,6 +1,6 @@
 --- ref-to-oneof.json
 +++ patched
-@@ -82,7 +82,12 @@
+@@ -127,7 +127,12 @@
              ]
            },
            "via_ref": {
diff --git a/tests/cases/simple/output/ref-to-redundant-wrapper.out b/tests/cases/simple/output/ref-to-redundant-wrapper.out
new file mode 100644
index 0000000..e068a3a
--- /dev/null
+++ b/tests/cases/simple/output/ref-to-redundant-wrapper.out
@@ -0,0 +1,36 @@
+--- ref-to-redundant-wrapper.json
++++ patched
+@@ -85,7 +85,13 @@
+             }
+           },
+           "nullable_via_ref": {
+-            "$ref": "#/components/schemas/NullableSubType"
++            "allOf": [
++              {
++                "$ref": "#/components/schemas/NullableSubType"
++              }
++            ],
++            "description": "Wrapped with redundant nullable.",
++            "nullable": true
+           },
+           "optional_field": {
+             "description": "An optional nullable field",
+
+
+Result for patch:
+[
+    Change {
+        message: "schema metadata added",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/nullable_via_ref",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/nullable_via_ref",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: Trivial,
+        details: Metadata,
+    },
+]
diff --git a/tests/cases/simple/output/ref-to-wrapper-nullable-added.out b/tests/cases/simple/output/ref-to-wrapper-nullable-added.out
new file mode 100644
index 0000000..e26ba2d
--- /dev/null
+++ b/tests/cases/simple/output/ref-to-wrapper-nullable-added.out
@@ -0,0 +1,35 @@
+--- ref-to-wrapper-nullable-added.json
++++ patched
+@@ -127,7 +127,12 @@
+             ]
+           },
+           "via_ref": {
+-            "$ref": "#/components/schemas/SubType"
++            "allOf": [
++              {
++                "$ref": "#/components/schemas/SubType"
++              }
++            ],
++            "nullable": true
+           }
+         },
+         "required": [
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable added at wrapper",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_ref",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_ref",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/remove-default-response.out b/tests/cases/simple/output/remove-default-response.out
index 615e057..2400966 100644
--- a/tests/cases/simple/output/remove-default-response.out
+++ b/tests/cases/simple/output/remove-default-response.out
@@ -1,6 +1,6 @@
 --- remove-default-response.json
 +++ patched
-@@ -442,16 +442,6 @@
+@@ -685,16 +685,6 @@
          "responses": {
            "200": {
              "description": "Success"
diff --git a/tests/cases/simple/output/remove-header-parameter.out b/tests/cases/simple/output/remove-header-parameter.out
index 3f5b122..516a2af 100644
--- a/tests/cases/simple/output/remove-header-parameter.out
+++ b/tests/cases/simple/output/remove-header-parameter.out
@@ -1,6 +1,6 @@
 --- remove-header-parameter.json
 +++ patched
-@@ -462,14 +462,6 @@
+@@ -705,14 +705,6 @@
          "operationId": "with_header",
          "parameters": [
            {
diff --git a/tests/cases/simple/output/remove-operation-parameter.out b/tests/cases/simple/output/remove-operation-parameter.out
index 7fc3327..e1c2fe1 100644
--- a/tests/cases/simple/output/remove-operation-parameter.out
+++ b/tests/cases/simple/output/remove-operation-parameter.out
@@ -1,11 +1,9 @@
 --- remove-operation-parameter.json
 +++ patched
-@@ -248,15 +248,6 @@
-             "schema": {
-               "type": "string"
+@@ -373,15 +373,6 @@
              }
--          },
--          {
+           },
+           {
 -            "description": "Language for the greeting",
 -            "in": "query",
 -            "name": "language",
@@ -13,9 +11,11 @@
 -            "schema": {
 -              "type": "string"
 -            }
-           }
-         ],
-         "responses": {
+-          },
+-          {
+             "description": "Output format (nullable for testing)",
+             "in": "query",
+             "name": "format",
 
 
 Result for patch:
diff --git a/tests/cases/simple/output/remove-operation.out b/tests/cases/simple/output/remove-operation.out
index 04ed3a9..fc389eb 100644
--- a/tests/cases/simple/output/remove-operation.out
+++ b/tests/cases/simple/output/remove-operation.out
@@ -1,6 +1,6 @@
 --- remove-operation.json
 +++ patched
-@@ -361,18 +361,7 @@
+@@ -576,18 +576,7 @@
          "summary": "Get oneOf schema"
        }
      },
diff --git a/tests/cases/simple/output/remove-optional-body.out b/tests/cases/simple/output/remove-optional-body.out
index 4a7a983..6887e87 100644
--- a/tests/cases/simple/output/remove-optional-body.out
+++ b/tests/cases/simple/output/remove-optional-body.out
@@ -1,6 +1,6 @@
 --- remove-optional-body.json
 +++ patched
-@@ -296,16 +296,6 @@
+@@ -429,16 +429,6 @@
        },
        "put": {
          "operationId": "update_item",
diff --git a/tests/cases/simple/output/remove-required-body.out b/tests/cases/simple/output/remove-required-body.out
index 8cb5edc..76be9c1 100644
--- a/tests/cases/simple/output/remove-required-body.out
+++ b/tests/cases/simple/output/remove-required-body.out
@@ -1,6 +1,6 @@
 --- remove-required-body.json
 +++ patched
-@@ -277,16 +277,6 @@
+@@ -410,16 +410,6 @@
      "/items": {
        "post": {
          "operationId": "create_item",
diff --git a/tests/cases/simple/output/remove-response-code.out b/tests/cases/simple/output/remove-response-code.out
index 6decf76..3dbf0d6 100644
--- a/tests/cases/simple/output/remove-response-code.out
+++ b/tests/cases/simple/output/remove-response-code.out
@@ -1,6 +1,6 @@
 --- remove-response-code.json
 +++ patched
-@@ -440,9 +440,6 @@
+@@ -683,9 +683,6 @@
        "get": {
          "operationId": "with_default",
          "responses": {
diff --git a/tests/cases/simple/output/remove-unnamed-operation.out b/tests/cases/simple/output/remove-unnamed-operation.out
index a895a32..a9cedb4 100644
--- a/tests/cases/simple/output/remove-unnamed-operation.out
+++ b/tests/cases/simple/output/remove-unnamed-operation.out
@@ -1,6 +1,6 @@
 --- remove-unnamed-operation.json
 +++ patched
-@@ -426,16 +426,6 @@
+@@ -669,16 +669,6 @@
          "summary": "Get typed properties"
        }
      },
diff --git a/tests/cases/simple/output/schema-kind-type-to-oneof.out b/tests/cases/simple/output/schema-kind-type-to-oneof.out
index f6591ab..8993af5 100644
--- a/tests/cases/simple/output/schema-kind-type-to-oneof.out
+++ b/tests/cases/simple/output/schema-kind-type-to-oneof.out
@@ -1,7 +1,7 @@
 --- schema-kind-type-to-oneof.json
 +++ patched
-@@ -135,12 +135,14 @@
-         "$ref": "#/components/schemas/SubType"
+@@ -256,12 +256,14 @@
+         "type": "object"
        },
        "SubType": {
 -        "properties": {
@@ -18,7 +18,7 @@
 +        ]
        },
        "Tree": {
-         "properties": {
+         "nullable": true,
 
 
 Result for patch:
@@ -39,4 +39,20 @@ Result for patch:
         class: Incompatible,
         details: Datatype,
     },
+    Change {
+        message: "schema kind changed from regular type to oneOf",
+        old_path: [
+            "#/components/schemas/SubType",
+            "#/components/schemas/CreateItem/properties/metadata_nullable/0/$ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/SubType",
+            "#/components/schemas/CreateItem/properties/metadata_nullable/0/$ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: Incompatible,
+        details: Datatype,
+    },
 ]
diff --git a/tests/cases/simple/output/shared-non-nullable-to-nullable.out b/tests/cases/simple/output/shared-non-nullable-to-nullable.out
new file mode 100644
index 0000000..f15fbaa
--- /dev/null
+++ b/tests/cases/simple/output/shared-non-nullable-to-nullable.out
@@ -0,0 +1,43 @@
+--- shared-non-nullable-to-nullable.json
++++ patched
+@@ -240,6 +240,7 @@
+       "SharedType": {
+         "properties": {
+           "data": {
++            "nullable": true,
+             "type": "string"
+           },
+           "id": {
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/components/schemas/SharedType/properties/data",
+            "#/paths/~1shared/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/SharedType/properties/data",
+            "#/paths/~1shared/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: ForwardIncompatible,
+        details: LessStrict,
+    },
+    Change {
+        message: "schema became nullable",
+        old_path: [
+            "#/components/schemas/SharedType/properties/data",
+            "#/paths/~1shared/post/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/SharedType/properties/data",
+            "#/paths/~1shared/post/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/shared-nullable-to-non-nullable.out b/tests/cases/simple/output/shared-nullable-to-non-nullable.out
new file mode 100644
index 0000000..4432bde
--- /dev/null
+++ b/tests/cases/simple/output/shared-nullable-to-non-nullable.out
@@ -0,0 +1,43 @@
+--- shared-nullable-to-non-nullable.json
++++ patched
+@@ -246,7 +246,6 @@
+             "type": "string"
+           },
+           "optional_data": {
+-            "nullable": true,
+             "type": "string"
+           }
+         },
+
+
+Result for patch:
+[
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/components/schemas/SharedType/properties/optional_data",
+            "#/paths/~1shared/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/SharedType/properties/optional_data",
+            "#/paths/~1shared/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: BackwardIncompatible,
+        details: MoreStrict,
+    },
+    Change {
+        message: "schema became non-nullable",
+        old_path: [
+            "#/components/schemas/SharedType/properties/optional_data",
+            "#/paths/~1shared/post/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/SharedType/properties/optional_data",
+            "#/paths/~1shared/post/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/string-format-change.out b/tests/cases/simple/output/string-format-change.out
index 1f8edf0..48f6a89 100644
--- a/tests/cases/simple/output/string-format-change.out
+++ b/tests/cases/simple/output/string-format-change.out
@@ -1,13 +1,13 @@
 --- string-format-change.json
 +++ patched
-@@ -50,6 +50,7 @@
+@@ -69,6 +69,7 @@
          "properties": {
            "message": {
              "description": "The greeting message",
 +            "format": "uuid",
              "type": "string"
            },
-           "not_a_number": {
+           "non_nullable_wrapper_of_nullable": {
 
 
 Result for patch:
diff --git a/tests/cases/simple/output/type-indirection.out b/tests/cases/simple/output/type-indirection.out
index 910cf39..a338a10 100644
--- a/tests/cases/simple/output/type-indirection.out
+++ b/tests/cases/simple/output/type-indirection.out
@@ -1,6 +1,6 @@
 --- type-indirection.json
 +++ patched
-@@ -49,8 +49,7 @@
+@@ -68,8 +68,7 @@
        "GreetingResponse": {
          "properties": {
            "message": {
@@ -8,9 +8,9 @@
 -            "type": "string"
 +            "$ref": "#/components/schemas/GreetingResponseMessage"
            },
-           "not_a_number": {
-             "not": {
-@@ -90,6 +89,13 @@
+           "non_nullable_wrapper_of_nullable": {
+             "allOf": [
+@@ -135,6 +134,13 @@
          ],
          "type": "object"
        },
diff --git a/tests/cases/simple/output/type-rename.out b/tests/cases/simple/output/type-rename.out
index bac28a3..b068a6f 100644
--- a/tests/cases/simple/output/type-rename.out
+++ b/tests/cases/simple/output/type-rename.out
@@ -1,6 +1,6 @@
 --- type-rename.json
 +++ patched
-@@ -46,7 +46,7 @@
+@@ -65,7 +65,7 @@
          ],
          "type": "object"
        },
@@ -9,7 +9,7 @@
          "properties": {
            "message": {
              "description": "The greeting message",
-@@ -264,7 +264,7 @@
+@@ -397,7 +397,7 @@
              "content": {
                "application/json": {
                  "schema": {
diff --git a/tests/cases/simple/output/unhandled-add-prop.out b/tests/cases/simple/output/unhandled-add-prop.out
index 37193a0..a0c94c8 100644
--- a/tests/cases/simple/output/unhandled-add-prop.out
+++ b/tests/cases/simple/output/unhandled-add-prop.out
@@ -1,8 +1,8 @@
 --- unhandled-add-prop.json
 +++ patched
-@@ -57,6 +57,10 @@
-               "type": "number"
-             }
+@@ -101,6 +101,10 @@
+             "description": "Nullable wrapper around already-nullable type.",
+             "nullable": true
            },
 +          "source": {
 +            "description": "Where the greeting originated",
@@ -11,7 +11,7 @@
            "via_allof": {
              "allOf": [
                {
-@@ -86,7 +90,8 @@
+@@ -131,7 +135,8 @@
            }
          },
          "required": [
diff --git a/tests/cases/simple/output/wrapper-non-nullable-to-nullable.out b/tests/cases/simple/output/wrapper-non-nullable-to-nullable.out
new file mode 100644
index 0000000..80b1793
--- /dev/null
+++ b/tests/cases/simple/output/wrapper-non-nullable-to-nullable.out
@@ -0,0 +1,31 @@
+--- wrapper-non-nullable-to-nullable.json
++++ patched
+@@ -107,7 +107,8 @@
+                 "$ref": "#/components/schemas/SubType"
+               }
+             ],
+-            "description": "Via allOf."
++            "description": "Via allOf.",
++            "nullable": true
+           },
+           "via_anyof": {
+             "anyOf": [
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable added at wrapper",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_allof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_allof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: BackwardIncompatible,
+        details: LessStrict,
+    },
+]
diff --git a/tests/cases/simple/output/wrapper-nullable-to-non-nullable.out b/tests/cases/simple/output/wrapper-nullable-to-non-nullable.out
new file mode 100644
index 0000000..dd42fa8
--- /dev/null
+++ b/tests/cases/simple/output/wrapper-nullable-to-non-nullable.out
@@ -0,0 +1,31 @@
+--- wrapper-nullable-to-non-nullable.json
++++ patched
+@@ -115,8 +115,7 @@
+                 "$ref": "#/components/schemas/SubType"
+               }
+             ],
+-            "description": "Via anyOf.",
+-            "nullable": true
++            "description": "Via anyOf."
+           },
+           "via_oneof": {
+             "description": "Via oneOf.",
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable removed from wrapper",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
+]
diff --git a/tests/cases/simple/output/wrapper-to-inline-nullable-removed.out b/tests/cases/simple/output/wrapper-to-inline-nullable-removed.out
new file mode 100644
index 0000000..e40dd73
--- /dev/null
+++ b/tests/cases/simple/output/wrapper-to-inline-nullable-removed.out
@@ -0,0 +1,54 @@
+--- wrapper-to-inline-nullable-removed.json
++++ patched
+@@ -110,13 +110,12 @@
+             "description": "Via allOf."
+           },
+           "via_anyof": {
+-            "anyOf": [
+-              {
+-                "$ref": "#/components/schemas/SubType"
++            "properties": {
++              "value": {
++                "type": "string"
+               }
+-            ],
+-            "description": "Via anyOf.",
+-            "nullable": true
++            },
++            "type": "object"
+           },
+           "via_oneof": {
+             "description": "Via oneOf.",
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable removed from wrapper",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
+    Change {
+        message: "schema metadata removed",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: Trivial,
+        details: Metadata,
+    },
+]
diff --git a/tests/cases/simple/output/wrapper-to-ref-nullable-removed.out b/tests/cases/simple/output/wrapper-to-ref-nullable-removed.out
new file mode 100644
index 0000000..554c26b
--- /dev/null
+++ b/tests/cases/simple/output/wrapper-to-ref-nullable-removed.out
@@ -0,0 +1,50 @@
+--- wrapper-to-ref-nullable-removed.json
++++ patched
+@@ -110,13 +110,7 @@
+             "description": "Via allOf."
+           },
+           "via_anyof": {
+-            "anyOf": [
+-              {
+-                "$ref": "#/components/schemas/SubType"
+-              }
+-            ],
+-            "description": "Via anyOf.",
+-            "nullable": true
++            "$ref": "#/components/schemas/SubType"
+           },
+           "via_oneof": {
+             "description": "Via oneOf.",
+
+
+Result for patch:
+[
+    Change {
+        message: "nullable removed from wrapper",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: ForwardIncompatible,
+        details: MoreStrict,
+    },
+    Change {
+        message: "schema metadata removed",
+        old_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/GreetingResponse/properties/via_anyof",
+            "#/paths/~1hello~1{name}/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: Trivial,
+        details: Metadata,
+    },
+]
diff --git a/tests/cases/simple/output/wrapper-unchanged-with-type-change.out b/tests/cases/simple/output/wrapper-unchanged-with-type-change.out
index 7b96447..c27e159 100644
--- a/tests/cases/simple/output/wrapper-unchanged-with-type-change.out
+++ b/tests/cases/simple/output/wrapper-unchanged-with-type-change.out
@@ -1,6 +1,6 @@
 --- wrapper-unchanged-with-type-change.json
 +++ patched
-@@ -137,7 +137,7 @@
+@@ -258,7 +258,7 @@
        "SubType": {
          "properties": {
            "value": {
@@ -29,4 +29,20 @@ Result for patch:
         class: Incompatible,
         details: UnknownDifference,
     },
+    Change {
+        message: "schema types changed",
+        old_path: [
+            "#/components/schemas/SubType/properties/value",
+            "#/components/schemas/CreateItem/properties/metadata_nullable/0/$ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/SubType/properties/value",
+            "#/components/schemas/CreateItem/properties/metadata_nullable/0/$ref",
+            "#/paths/~1items/post/request_body/content/application~1json/schema/$ref",
+        ],
+        comparison: Input,
+        class: Incompatible,
+        details: UnknownDifference,
+    },
 ]
diff --git a/tests/cases/simple/patch/additional-props-non-nullable-to-nullable.json b/tests/cases/simple/patch/additional-props-non-nullable-to-nullable.json
new file mode 100644
index 0000000..b23fe9b
--- /dev/null
+++ b/tests/cases/simple/patch/additional-props-non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/ObjectWithConstraints/additionalProperties/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/array-items-non-nullable-to-nullable.json b/tests/cases/simple/patch/array-items-non-nullable-to-nullable.json
new file mode 100644
index 0000000..05e83ce
--- /dev/null
+++ b/tests/cases/simple/patch/array-items-non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/ArrayWithConstraints/items/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/array-items-remove.json b/tests/cases/simple/patch/array-items-remove.json
index 18f0cf9..03f7bf6 100644
--- a/tests/cases/simple/patch/array-items-remove.json
+++ b/tests/cases/simple/patch/array-items-remove.json
@@ -3,7 +3,8 @@
     "op": "add",
     "path": "/components/schemas/Tree/properties/children/items",
     "value": {
-      "type": "string"
+      "type": "string",
+      "nullable": true
     }
   }
 ]
diff --git a/tests/cases/simple/patch/boolean-enum-change.json b/tests/cases/simple/patch/boolean-enum-change.json
index ea478de..b776c97 100644
--- a/tests/cases/simple/patch/boolean-enum-change.json
+++ b/tests/cases/simple/patch/boolean-enum-change.json
@@ -2,6 +2,8 @@
   {
     "op": "add",
     "path": "/components/schemas/TypedProperties/properties/enabled/enum",
-    "value": [true]
+    "value": [
+      true
+    ]
   }
 ]
diff --git a/tests/cases/simple/patch/change-operation-parameter-requirement.json b/tests/cases/simple/patch/change-operation-parameter-requirement.json
index cf46c17..ece6f73 100644
--- a/tests/cases/simple/patch/change-operation-parameter-requirement.json
+++ b/tests/cases/simple/patch/change-operation-parameter-requirement.json
@@ -1,12 +1,12 @@
 [
-	{
-		"op": "test",
-		"path": "/paths/~1hello~1{name}/get/parameters/1/name",
-		"value": "language"
-	},
-	{
-		"op": "replace",
-		"path": "/paths/~1hello~1{name}/get/parameters/1/required",
-		"value": true
-	}
+  {
+    "op": "test",
+    "path": "/paths/~1hello~1{name}/get/parameters/1/name",
+    "value": "language"
+  },
+  {
+    "op": "replace",
+    "path": "/paths/~1hello~1{name}/get/parameters/1/required",
+    "value": true
+  }
 ]
diff --git a/tests/cases/simple/patch/change-operation-parameter-type.json b/tests/cases/simple/patch/change-operation-parameter-type.json
index 76ea4cf..17bdbd2 100644
--- a/tests/cases/simple/patch/change-operation-parameter-type.json
+++ b/tests/cases/simple/patch/change-operation-parameter-type.json
@@ -1,12 +1,12 @@
 [
-	{
-		"op": "test",
-		"path": "/paths/~1hello~1{name}/get/parameters/1/name",
-		"value": "language"
-	},
-	{
-		"op": "replace",
-		"path": "/paths/~1hello~1{name}/get/parameters/1/schema/type",
-		"value": "integer"
-	}
+  {
+    "op": "test",
+    "path": "/paths/~1hello~1{name}/get/parameters/1/name",
+    "value": "language"
+  },
+  {
+    "op": "replace",
+    "path": "/paths/~1hello~1{name}/get/parameters/1/schema/type",
+    "value": "integer"
+  }
 ]
diff --git a/tests/cases/simple/patch/change-property-type.json b/tests/cases/simple/patch/change-property-type.json
index e91d4fb..7307e9d 100644
--- a/tests/cases/simple/patch/change-property-type.json
+++ b/tests/cases/simple/patch/change-property-type.json
@@ -1,7 +1,7 @@
 [
-	{
-		"op": "replace",
-		"path": "/components/schemas/GreetingResponse/properties/message/type",
-		"value": "integer"
-	}
+  {
+    "op": "replace",
+    "path": "/components/schemas/GreetingResponse/properties/message/type",
+    "value": "integer"
+  }
 ]
diff --git a/tests/cases/simple/patch/inline-to-wrapper-nullable-added.json b/tests/cases/simple/patch/inline-to-wrapper-nullable-added.json
new file mode 100644
index 0000000..a7ab545
--- /dev/null
+++ b/tests/cases/simple/patch/inline-to-wrapper-nullable-added.json
@@ -0,0 +1,15 @@
+[
+  {
+    "op": "replace",
+    "path": "/components/schemas/GreetingResponse/properties/message",
+    "value": {
+      "nullable": true,
+      "description": "The greeting message",
+      "allOf": [
+        {
+          "type": "string"
+        }
+      ]
+    }
+  }
+]
diff --git a/tests/cases/simple/patch/input-non-nullable-to-nullable.json b/tests/cases/simple/patch/input-non-nullable-to-nullable.json
new file mode 100644
index 0000000..bd8929f
--- /dev/null
+++ b/tests/cases/simple/patch/input-non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/CreateItem/properties/name/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/input-nullable-to-non-nullable.json b/tests/cases/simple/patch/input-nullable-to-non-nullable.json
new file mode 100644
index 0000000..c4c8f12
--- /dev/null
+++ b/tests/cases/simple/patch/input-nullable-to-non-nullable.json
@@ -0,0 +1,6 @@
+[
+  {
+    "op": "remove",
+    "path": "/components/schemas/CreateItem/properties/description/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/input-ref-to-wrapper-nullable-added.json b/tests/cases/simple/patch/input-ref-to-wrapper-nullable-added.json
new file mode 100644
index 0000000..a4ca909
--- /dev/null
+++ b/tests/cases/simple/patch/input-ref-to-wrapper-nullable-added.json
@@ -0,0 +1,14 @@
+[
+  {
+    "op": "replace",
+    "path": "/components/schemas/CreateItem/properties/name",
+    "value": {
+      "nullable": true,
+      "allOf": [
+        {
+          "type": "string"
+        }
+      ]
+    }
+  }
+]
diff --git a/tests/cases/simple/patch/input-root-non-nullable-to-nullable.json b/tests/cases/simple/patch/input-root-non-nullable-to-nullable.json
new file mode 100644
index 0000000..a97cea1
--- /dev/null
+++ b/tests/cases/simple/patch/input-root-non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/CreateItem/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/input-root-nullable-to-non-nullable.json b/tests/cases/simple/patch/input-root-nullable-to-non-nullable.json
new file mode 100644
index 0000000..c877cb9
--- /dev/null
+++ b/tests/cases/simple/patch/input-root-nullable-to-non-nullable.json
@@ -0,0 +1,6 @@
+[
+  {
+    "op": "remove",
+    "path": "/components/schemas/UpdateItem/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/input-wrapper-non-nullable-to-nullable.json b/tests/cases/simple/patch/input-wrapper-non-nullable-to-nullable.json
new file mode 100644
index 0000000..ec0d68a
--- /dev/null
+++ b/tests/cases/simple/patch/input-wrapper-non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/CreateItem/properties/metadata_ref/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/input-wrapper-nullable-to-non-nullable.json b/tests/cases/simple/patch/input-wrapper-nullable-to-non-nullable.json
new file mode 100644
index 0000000..370e915
--- /dev/null
+++ b/tests/cases/simple/patch/input-wrapper-nullable-to-non-nullable.json
@@ -0,0 +1,6 @@
+[
+  {
+    "op": "remove",
+    "path": "/components/schemas/CreateItem/properties/metadata_nullable/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/input-wrapper-to-ref-nullable-removed.json b/tests/cases/simple/patch/input-wrapper-to-ref-nullable-removed.json
new file mode 100644
index 0000000..017467b
--- /dev/null
+++ b/tests/cases/simple/patch/input-wrapper-to-ref-nullable-removed.json
@@ -0,0 +1,9 @@
+[
+  {
+    "op": "replace",
+    "path": "/components/schemas/CreateItem/properties/metadata_nullable",
+    "value": {
+      "$ref": "#/components/schemas/SubType"
+    }
+  }
+]
diff --git a/tests/cases/simple/patch/nested-wrapper-non-nullable-to-nullable.json b/tests/cases/simple/patch/nested-wrapper-non-nullable-to-nullable.json
new file mode 100644
index 0000000..44bc6ea
--- /dev/null
+++ b/tests/cases/simple/patch/nested-wrapper-non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/NestedWrapperC/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/nested-wrapper-nullable-to-non-nullable.json b/tests/cases/simple/patch/nested-wrapper-nullable-to-non-nullable.json
new file mode 100644
index 0000000..482f8e4
--- /dev/null
+++ b/tests/cases/simple/patch/nested-wrapper-nullable-to-non-nullable.json
@@ -0,0 +1,6 @@
+[
+  {
+    "op": "remove",
+    "path": "/components/schemas/NestedNullableWrapperC/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/non-nullable-to-nullable.json b/tests/cases/simple/patch/non-nullable-to-nullable.json
new file mode 100644
index 0000000..89951c6
--- /dev/null
+++ b/tests/cases/simple/patch/non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/GreetingResponse/properties/message/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/nullable-to-non-nullable.json b/tests/cases/simple/patch/nullable-to-non-nullable.json
new file mode 100644
index 0000000..efcc0df
--- /dev/null
+++ b/tests/cases/simple/patch/nullable-to-non-nullable.json
@@ -0,0 +1,6 @@
+[
+  {
+    "op": "remove",
+    "path": "/components/schemas/GreetingResponse/properties/optional_field/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/output-root-non-nullable-to-nullable.json b/tests/cases/simple/patch/output-root-non-nullable-to-nullable.json
new file mode 100644
index 0000000..1921546
--- /dev/null
+++ b/tests/cases/simple/patch/output-root-non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/GreetingResponse/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/output-root-nullable-to-non-nullable.json b/tests/cases/simple/patch/output-root-nullable-to-non-nullable.json
new file mode 100644
index 0000000..3b631e2
--- /dev/null
+++ b/tests/cases/simple/patch/output-root-nullable-to-non-nullable.json
@@ -0,0 +1,6 @@
+[
+  {
+    "op": "remove",
+    "path": "/components/schemas/Tree/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/param-non-nullable-to-nullable.json b/tests/cases/simple/patch/param-non-nullable-to-nullable.json
new file mode 100644
index 0000000..e3ec2fb
--- /dev/null
+++ b/tests/cases/simple/patch/param-non-nullable-to-nullable.json
@@ -0,0 +1,12 @@
+[
+  {
+    "op": "test",
+    "path": "/paths/~1hello~1{name}/get/parameters/1/name",
+    "value": "language"
+  },
+  {
+    "op": "add",
+    "path": "/paths/~1hello~1{name}/get/parameters/1/schema/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/param-nullable-to-non-nullable.json b/tests/cases/simple/patch/param-nullable-to-non-nullable.json
new file mode 100644
index 0000000..8278722
--- /dev/null
+++ b/tests/cases/simple/patch/param-nullable-to-non-nullable.json
@@ -0,0 +1,11 @@
+[
+  {
+    "op": "test",
+    "path": "/paths/~1hello~1{name}/get/parameters/2/name",
+    "value": "format"
+  },
+  {
+    "op": "remove",
+    "path": "/paths/~1hello~1{name}/get/parameters/2/schema/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/redundant-wrapper-nullable-added.json b/tests/cases/simple/patch/redundant-wrapper-nullable-added.json
new file mode 100644
index 0000000..e8cd80a
--- /dev/null
+++ b/tests/cases/simple/patch/redundant-wrapper-nullable-added.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/GreetingResponse/properties/non_nullable_wrapper_of_nullable/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/redundant-wrapper-nullable-removed.json b/tests/cases/simple/patch/redundant-wrapper-nullable-removed.json
new file mode 100644
index 0000000..62ded33
--- /dev/null
+++ b/tests/cases/simple/patch/redundant-wrapper-nullable-removed.json
@@ -0,0 +1,6 @@
+[
+  {
+    "op": "remove",
+    "path": "/components/schemas/GreetingResponse/properties/redundant_nullable_wrapper/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/redundant-wrapper-to-ref.json b/tests/cases/simple/patch/redundant-wrapper-to-ref.json
new file mode 100644
index 0000000..548973e
--- /dev/null
+++ b/tests/cases/simple/patch/redundant-wrapper-to-ref.json
@@ -0,0 +1,9 @@
+[
+  {
+    "op": "replace",
+    "path": "/components/schemas/GreetingResponse/properties/redundant_nullable_wrapper",
+    "value": {
+      "$ref": "#/components/schemas/NullableSubType"
+    }
+  }
+]
diff --git a/tests/cases/simple/patch/ref-to-redundant-wrapper.json b/tests/cases/simple/patch/ref-to-redundant-wrapper.json
new file mode 100644
index 0000000..191fbd2
--- /dev/null
+++ b/tests/cases/simple/patch/ref-to-redundant-wrapper.json
@@ -0,0 +1,15 @@
+[
+  {
+    "op": "replace",
+    "path": "/components/schemas/GreetingResponse/properties/nullable_via_ref",
+    "value": {
+      "nullable": true,
+      "description": "Wrapped with redundant nullable.",
+      "allOf": [
+        {
+          "$ref": "#/components/schemas/NullableSubType"
+        }
+      ]
+    }
+  }
+]
diff --git a/tests/cases/simple/patch/ref-to-wrapper-nullable-added.json b/tests/cases/simple/patch/ref-to-wrapper-nullable-added.json
new file mode 100644
index 0000000..7e17eb0
--- /dev/null
+++ b/tests/cases/simple/patch/ref-to-wrapper-nullable-added.json
@@ -0,0 +1,14 @@
+[
+  {
+    "op": "replace",
+    "path": "/components/schemas/GreetingResponse/properties/via_ref",
+    "value": {
+      "nullable": true,
+      "allOf": [
+        {
+          "$ref": "#/components/schemas/SubType"
+        }
+      ]
+    }
+  }
+]
diff --git a/tests/cases/simple/patch/remove-operation-parameter.json b/tests/cases/simple/patch/remove-operation-parameter.json
index 32fb971..c45f2ae 100644
--- a/tests/cases/simple/patch/remove-operation-parameter.json
+++ b/tests/cases/simple/patch/remove-operation-parameter.json
@@ -1,6 +1,6 @@
 [
-	{
-		"op": "remove",
-		"path": "/paths/~1hello~1{name}/get/parameters/1"
-	}
+  {
+    "op": "remove",
+    "path": "/paths/~1hello~1{name}/get/parameters/1"
+  }
 ]
diff --git a/tests/cases/simple/patch/shared-non-nullable-to-nullable.json b/tests/cases/simple/patch/shared-non-nullable-to-nullable.json
new file mode 100644
index 0000000..4435690
--- /dev/null
+++ b/tests/cases/simple/patch/shared-non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/SharedType/properties/data/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/shared-nullable-to-non-nullable.json b/tests/cases/simple/patch/shared-nullable-to-non-nullable.json
new file mode 100644
index 0000000..f591e4f
--- /dev/null
+++ b/tests/cases/simple/patch/shared-nullable-to-non-nullable.json
@@ -0,0 +1,6 @@
+[
+  {
+    "op": "remove",
+    "path": "/components/schemas/SharedType/properties/optional_data/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/unhandled-add-prop.json b/tests/cases/simple/patch/unhandled-add-prop.json
index ad68b05..d62e1f9 100644
--- a/tests/cases/simple/patch/unhandled-add-prop.json
+++ b/tests/cases/simple/patch/unhandled-add-prop.json
@@ -1,15 +1,15 @@
 [
-	{
-		"op": "add",
-		"path": "/components/schemas/GreetingResponse/properties/source",
-		"value": {
-			"type": "string",
-			"description": "Where the greeting originated"
-		}
-	},
-	{
-		"op": "add",
-		"path": "/components/schemas/GreetingResponse/required/-",
-		"value": "source"
-	}
+  {
+    "op": "add",
+    "path": "/components/schemas/GreetingResponse/properties/source",
+    "value": {
+      "type": "string",
+      "description": "Where the greeting originated"
+    }
+  },
+  {
+    "op": "add",
+    "path": "/components/schemas/GreetingResponse/required/-",
+    "value": "source"
+  }
 ]
diff --git a/tests/cases/simple/patch/wrapper-non-nullable-to-nullable.json b/tests/cases/simple/patch/wrapper-non-nullable-to-nullable.json
new file mode 100644
index 0000000..fc3b039
--- /dev/null
+++ b/tests/cases/simple/patch/wrapper-non-nullable-to-nullable.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "add",
+    "path": "/components/schemas/GreetingResponse/properties/via_allof/nullable",
+    "value": true
+  }
+]
diff --git a/tests/cases/simple/patch/wrapper-nullable-to-non-nullable.json b/tests/cases/simple/patch/wrapper-nullable-to-non-nullable.json
new file mode 100644
index 0000000..d783701
--- /dev/null
+++ b/tests/cases/simple/patch/wrapper-nullable-to-non-nullable.json
@@ -0,0 +1,6 @@
+[
+  {
+    "op": "remove",
+    "path": "/components/schemas/GreetingResponse/properties/via_anyof/nullable"
+  }
+]
diff --git a/tests/cases/simple/patch/wrapper-to-inline-nullable-removed.json b/tests/cases/simple/patch/wrapper-to-inline-nullable-removed.json
new file mode 100644
index 0000000..da43834
--- /dev/null
+++ b/tests/cases/simple/patch/wrapper-to-inline-nullable-removed.json
@@ -0,0 +1,14 @@
+[
+  {
+    "op": "replace",
+    "path": "/components/schemas/GreetingResponse/properties/via_anyof",
+    "value": {
+      "type": "object",
+      "properties": {
+        "value": {
+          "type": "string"
+        }
+      }
+    }
+  }
+]
diff --git a/tests/cases/simple/patch/wrapper-to-ref-nullable-removed.json b/tests/cases/simple/patch/wrapper-to-ref-nullable-removed.json
new file mode 100644
index 0000000..20c364b
--- /dev/null
+++ b/tests/cases/simple/patch/wrapper-to-ref-nullable-removed.json
@@ -0,0 +1,9 @@
+[
+  {
+    "op": "replace",
+    "path": "/components/schemas/GreetingResponse/properties/via_anyof",
+    "value": {
+      "$ref": "#/components/schemas/SubType"
+    }
+  }
+]