diff --git a/Lib/pydoc.py b/Lib/pydoc.py
index 292aa46015e..4d681b0efa9 100755
--- a/Lib/pydoc.py
+++ b/Lib/pydoc.py
@@ -132,7 +132,10 @@ def stripid(text):
     return _re_stripid.sub(r'\1', text)
 
 def _is_some_method(obj):
-    return inspect.ismethod(obj) or inspect.ismethoddescriptor(obj)
+    return (inspect.isfunction(obj) or
+            inspect.ismethod(obj) or
+            inspect.isbuiltin(obj) or
+            inspect.ismethoddescriptor(obj))
 
 def allmethods(cl):
     methods = {}
diff --git a/Lib/test/test_pydoc.py b/Lib/test/test_pydoc.py
index aa8baf723ca..8adcdd87a48 100644
--- a/Lib/test/test_pydoc.py
+++ b/Lib/test/test_pydoc.py
@@ -420,6 +420,30 @@ class PydocDocTest(unittest.TestCase):
             self.assertTrue(pydoc.ispackage(test_dir))
             os.remove(init_path)
 
+    def test_allmethods(self):
+        # issue 17476: allmethods was no longer returning unbound methods.
+        # This test is a bit fragile in the face of changes to object and type,
+        # but I can't think of a better way to do it without duplicating the
+        # logic of the function under test.
+
+        class TestClass(object):
+            def method_returning_true(self):
+                return True
+
+        # What we expect to get back: everything on object...
+        expected = dict(vars(object))
+        # ...plus our unbound method...
+        expected['method_returning_true'] = TestClass.method_returning_true
+        # ...but not the non-methods on object.
+        del expected['__doc__']
+        del expected['__class__']
+        # inspect resolves descriptors on type into methods, but vars doesn't,
+        # so we need to update __subclasshook__.
+        expected['__subclasshook__'] = TestClass.__subclasshook__
+
+        methods = pydoc.allmethods(TestClass)
+        self.assertDictEqual(methods, expected)
+
 
 class PydocImportTest(unittest.TestCase):
 
diff --git a/Misc/NEWS b/Misc/NEWS
index d69146337c1..cb5eedf1140 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -289,6 +289,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #17476: Fixed regression relative to Python2 in undocumented pydoc
+  'allmethods'; it was missing unbound methods on the class.
+
 - Issue #17474: Remove the deprecated methods of Request class.
 
 - Issue #16709: unittest discover order is no-longer filesystem specific. Patch