diff --git a/src/lazy.jl b/src/lazy.jl
index e122699..cf08cc6 100644
--- a/src/lazy.jl
+++ b/src/lazy.jl
@@ -587,8 +587,23 @@ isbigfloat(x::NumberResult) = x.tag == BIGFLOAT
     b = getbyte(buf, pos)
     startpos = pos
     isneg = isfloat = overflow = false
-    if !opts.allownan
+    if opts.allownan
+        # If this doesn't start like an integer, let Parsers handle
+        # NaN/Inf/-Inf and the configured special values.
+        if b == UInt8('-') || b == UInt8('+')
+            if pos == len
+                error = UnexpectedEOF
+                @goto invalid
+            end
+            b = getbyte(buf, pos + 1)
+            isfloat = !(UInt8('0') <= b <= UInt8('9'))
+        else
+            isfloat = !(UInt8('0') <= b <= UInt8('9'))
+        end
+    end
+    if !isfloat
         val = Int64(0)
+        b = getbyte(buf, pos)
         isneg = b == UInt8('-')
         if isneg || b == UInt8('+') # spec doesn't allow leading +, but we do
             pos += 1
@@ -652,7 +667,8 @@ isbigfloat(x::NumberResult) = x.tag == BIGFLOAT
             end
         end
     end
-    if isfloat || opts.allownan
+
+    if isfloat
         if opts.allownan
             # check for NaN, Inf, -Inf
             @check_special(opts.nan, NaN)
diff --git a/test/parse.jl b/test/parse.jl
index bbea56b..6a4234d 100644
--- a/test/parse.jl
+++ b/test/parse.jl
@@ -187,6 +187,11 @@ end
     foo::String = "bar"
 end
 
+#struct for parsing typemax Int test
+struct TestAllownanInt
+    a::Int64
+end
+
 # example from JSON.parse docstring
 abstract type AbstractMonster end
 
@@ -406,7 +411,25 @@ JSON.lift(::DateMaterializedObjectStyle, ::Type{Date}, x::JSON.Object) = Date(x[
     @test_throws ArgumentError JSON.parse("trub")
     # allownan for parsing normally invalid json values
     @test JSON.parse("NaN"; allownan=true) === NaN
-    @test JSON.parse("Inf"; inf="Inf", allownan=true) === Inf
+    @test JSON.parse("Infinity"; allownan=true) === Inf
+    @test JSON.parse("-Infinity"; allownan=true) === -Inf
+    @test JSON.parse("Inf"; allownan=true) === Inf
+    @test JSON.parse("-Inf"; allownan=true) === -Inf
+    # Nested version
+    @test isequal(JSON.parse("[Inf,NaN,-Infinity]"; allownan=true), [Inf, NaN, -Inf])
+    # allownan with typemax Int
+    @test JSON.parse(string(typemax(Int)), Int; allownan=true) === typemax(Int) 
+    @test JSON.parse(string(typemax(UInt64)), UInt64; allownan=true) === typemax(UInt64) 
+    @test JSON.parse(string(typemax(Int64)), Int64; allownan=true) === typemax(Int64)
+    @test JSON.parse(string(typemin(Int64)), Int64; allownan=true) === typemin(Int64) 
+    @test JSON.parse(string(typemax(Int64)); allownan=true) === typemax(Int64) 
+    @test JSON.parse(string(typemax(Int128)), Int128; allownan=true) === typemax(Int128)
+    @test JSON.parse(string(2^53 + 1); allownan=true) === Int64(2^53 + 1)
+    #allownan with typemax in struct
+    @test JSON.parse("{\"a\":$(typemax(Int64))}", TestAllownanInt; allownan=true).a === typemax(Int64)
+    #Test that parsing "-" and "+" with allownan=true throws an error
+    @test_throws ArgumentError JSON.parse("-"; allownan=true)
+    @test_throws ArgumentError JSON.parse("+"; allownan=true)
     # jsonlines support
     @test JSON.parse("1"; jsonlines=true) == [1]
     @test JSON.parse("1 \t"; jsonlines=true) == [1]