diff --git a/tests/test_compat.py b/tests/test_compat.py
index 0e2e424cb..308c35dbd 100644
--- a/tests/test_compat.py
+++ b/tests/test_compat.py
@@ -1,4 +1,10 @@
-from click._compat import should_strip_ansi
+from __future__ import annotations
+
+import sys
+
+import pytest
+
+import click
 
 
 def test_is_jupyter_kernel_output():
@@ -7,4 +13,43 @@ class JupyterKernelFakeStream:
 
     # implementation detail, aka cheapskate test
     JupyterKernelFakeStream.__module__ = "ipykernel.faked"
-    assert not should_strip_ansi(stream=JupyterKernelFakeStream())
+    assert click._compat._is_jupyter_kernel_output(stream=JupyterKernelFakeStream())
+
+
+@pytest.mark.parametrize(
+    "stream",
+    [None, sys.stdin, sys.stderr, sys.stdout],
+)
+@pytest.mark.parametrize(
+    "color,expected_override",
+    [
+        (True, False),
+        (False, True),
+        (None, None),
+    ],
+)
+@pytest.mark.parametrize(
+    "isatty,is_jupyter,expected",
+    [
+        (True, False, False),
+        (False, True, False),
+        (False, False, True),
+    ],
+)
+def test_should_strip_ansi(
+    monkeypatch,
+    stream,
+    color: bool | None,
+    expected_override: bool | None,
+    isatty: bool,
+    is_jupyter: bool,
+    expected: bool,
+) -> None:
+    monkeypatch.setattr(click._compat, "isatty", lambda x: isatty)
+    monkeypatch.setattr(
+        click._compat, "_is_jupyter_kernel_output", lambda x: is_jupyter
+    )
+
+    if expected_override is not None:
+        expected = expected_override
+    assert click._compat.should_strip_ansi(stream=stream, color=color) == expected
diff --git a/tests/test_utils.py b/tests/test_utils.py
index d80aee716..657e37c92 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -207,8 +207,8 @@ def test_echo_via_pager(monkeypatch, capfd, cat, test):
 
 
 def test_echo_color_flag(monkeypatch, capfd):
-    isatty = True
-    monkeypatch.setattr(click._compat, "isatty", lambda x: isatty)
+    should_strip_ansi = False
+    monkeypatch.setattr(click._compat, "should_strip_ansi", lambda x: should_strip_ansi)
 
     text = "foo"
     styled_text = click.style(text, fg="red")
@@ -222,12 +222,12 @@ def test_echo_color_flag(monkeypatch, capfd):
     out, err = capfd.readouterr()
     assert out == f"{styled_text}\n"
 
-    isatty = True
+    should_strip_ansi = False
     click.echo(styled_text)
     out, err = capfd.readouterr()
     assert out == f"{styled_text}\n"
 
-    isatty = False
+    should_strip_ansi = True
     # Faking isatty() is not enough on Windows;
     # the implementation caches the colorama wrapped stream
     # so we have to use a new stream for each test