diff -r 1a6cb184e939 Lib/inspect.py
--- a/Lib/inspect.py	Mon Jan 28 13:26:25 2013 +0200
+++ b/Lib/inspect.py	Fri Feb 08 16:48:33 2013 +0100
@@ -1360,7 +1360,7 @@
     else:
         return signature(wrapped)
 
-    if isinstance(obj, types.FunctionType):
+    if isfunction(obj):
         return Signature.from_function(obj)
 
     if isinstance(obj, functools.partial):
@@ -1438,7 +1438,7 @@
         # __call__, __new__, or __init__ methods
         return sig.replace(parameters=tuple(sig.parameters.values())[1:])
 
-    if isinstance(obj, types.BuiltinFunctionType):
+    if isbuiltin(obj):
         # Raise a nicer error message for builtins
         msg = 'no signature found for builtin function {!r}'.format(obj)
         raise ValueError(msg)
@@ -1775,9 +1775,6 @@
     def from_function(cls, func):
         '''Constructs Signature for the given python function'''
 
-        if not isinstance(func, types.FunctionType):
-            raise TypeError('{!r} is not a Python function'.format(func))
-
         Parameter = cls._parameter_cls
 
         # Parameter information.
diff -r 1a6cb184e939 Lib/test/test_inspect.py
--- a/Lib/test/test_inspect.py	Mon Jan 28 13:26:25 2013 +0200
+++ b/Lib/test/test_inspect.py	Fri Feb 08 16:48:33 2013 +0100
@@ -1456,9 +1456,23 @@
         with self.assertRaisesRegex(TypeError, 'is not a callable object'):
             inspect.signature(42)
 
-        with self.assertRaisesRegex(TypeError, 'is not a Python function'):
+        with self.assertRaisesRegex(AttributeError, 'int.*object has no attribute.*__code__'):
             inspect.Signature.from_function(42)
 
+    def test_signature_from_functionlike_object(self):
+        def func(a,b, *args, kwonly=True, kwonlyreq, **kwargs):
+            pass
+
+        class funclike:
+            __code__ = func.__code__
+            __annotations__ = func.__annotations__
+            __defaults__ = func.__defaults__
+            __kwdefaults__ = func.__kwdefaults__
+
+        sig_func = inspect.Signature.from_function(func)
+        sig_funclike = inspect.Signature.from_function(funclike())
+        self.assertEqual(sig_funclike, sig_func)
+
     def test_signature_on_method(self):
         class Test:
             def foo(self, arg1, arg2=1) -> int: