diff --git a/Lib/test/test_decorators.py b/Lib/test/test_decorators.py
index 298979e..7d0243a 100644
--- a/Lib/test/test_decorators.py
+++ b/Lib/test/test_decorators.py
@@ -1,3 +1,4 @@
+from test import support
 import unittest
 
 def funcattrs(**kwds):
@@ -76,11 +77,28 @@ def foo(): return 42
         self.assertEqual(C.foo(), 42)
         self.assertEqual(C().foo(), 42)
 
-    def test_staticmethod_function(self):
-        @staticmethod
-        def notamethod(x):
+    def check_wrapper_attrs(self, method_wrapper, format_str):
+        def func(x):
             return x
-        self.assertRaises(TypeError, notamethod, 1)
+        wrapper = method_wrapper(func)
+
+        self.assertIs(wrapper.__func__, func)
+        self.assertIs(wrapper.__wrapped__, func)
+
+        for attr in ('__module__', '__qualname__', '__name__',
+                     '__doc__', '__annotations__'):
+            self.assertIs(getattr(wrapper, attr),
+                          getattr(func, attr))
+
+        self.assertEqual(repr(wrapper), format_str.format(func))
+
+        self.assertRaises(TypeError, wrapper, 1)
+
+    def test_staticmethod(self):
+        self.check_wrapper_attrs(staticmethod, '<staticmethod({!r})>')
+
+    def test_classmethod(self):
+        self.check_wrapper_attrs(classmethod, '<classmethod({!r})>')
 
     def test_dotted(self):
         decorators = MiscDecorators()
diff --git a/Lib/test/test_descr.py b/Lib/test/test_descr.py
index 8c75ec3..79d6c4b 100644
--- a/Lib/test/test_descr.py
+++ b/Lib/test/test_descr.py
@@ -1545,7 +1545,9 @@ class D(C):
         self.assertEqual(d.foo(1), (d, 1))
         self.assertEqual(D.foo(d, 1), (d, 1))
         # Test for a specific crash (SF bug 528132)
-        def f(cls, arg): return (cls, arg)
+        def f(cls, arg):
+            "f docstring"
+            return (cls, arg)
         ff = classmethod(f)
         self.assertEqual(ff.__get__(0, int)(42), (int, 42))
         self.assertEqual(ff.__get__(0)(42), (int, 42))
@@ -1571,10 +1573,16 @@ def f(cls, arg): return (cls, arg)
             self.fail("classmethod shouldn't accept keyword args")
 
         cm = classmethod(f)
-        self.assertEqual(cm.__dict__, {})
+        cm_dict = {'__annotations__': {},
+                   '__doc__': "f docstring",
+                   '__module__': __name__,
+                   '__name__': 'f',
+                   '__qualname__': f.__qualname__}
+        self.assertEqual(cm.__dict__, cm_dict)
+
         cm.x = 42
         self.assertEqual(cm.x, 42)
-        self.assertEqual(cm.__dict__, {"x" : 42})
+        self.assertEqual(cm.__dict__, {"x" : 42, **cm_dict})
         del cm.x
         self.assertNotHasAttr(cm, "x")
 
@@ -1654,10 +1662,10 @@ class D(C):
         self.assertEqual(d.foo(1), (d, 1))
         self.assertEqual(D.foo(d, 1), (d, 1))
         sm = staticmethod(None)
-        self.assertEqual(sm.__dict__, {})
+        self.assertEqual(sm.__dict__, {'__doc__': None})
         sm.x = 42
         self.assertEqual(sm.x, 42)
-        self.assertEqual(sm.__dict__, {"x" : 42})
+        self.assertEqual(sm.__dict__, {"x" : 42, '__doc__': None})
         del sm.x
         self.assertNotHasAttr(sm, "x")
 
diff --git a/Lib/test/test_pydoc.py b/Lib/test/test_pydoc.py
index 61575b5..e94ebd3 100644
--- a/Lib/test/test_pydoc.py
+++ b/Lib/test/test_pydoc.py
@@ -1142,7 +1142,8 @@ def sm(x, y):
                 '''A static method'''
                 ...
         self.assertEqual(self._get_summary_lines(X.__dict__['sm']),
-                         "<staticmethod object>")
+                         'sm(...)\n'
+                         '    A static method\n')
         self.assertEqual(self._get_summary_lines(X.sm), """\
 sm(x, y)
     A static method
@@ -1162,7 +1163,8 @@ def cm(cls, x):
                 '''A class method'''
                 ...
         self.assertEqual(self._get_summary_lines(X.__dict__['cm']),
-                         "<classmethod object>")
+                         'cm(...)\n'
+                         '    A class method\n')
         self.assertEqual(self._get_summary_lines(X.cm), """\
 cm(x) method of builtins.type instance
     A class method
diff --git a/Lib/test/test_reprlib.py b/Lib/test/test_reprlib.py
index a328810..0555b71 100644
--- a/Lib/test/test_reprlib.py
+++ b/Lib/test/test_reprlib.py
@@ -203,9 +203,9 @@ def test_descriptors(self):
         class C:
             def foo(cls): pass
         x = staticmethod(C.foo)
-        self.assertTrue(repr(x).startswith('<staticmethod object at 0x'))
+        self.assertEqual(repr(x), f'<staticmethod({C.foo!r})>')
         x = classmethod(C.foo)
-        self.assertTrue(repr(x).startswith('<classmethod object at 0x'))
+        self.assertEqual(repr(x), f'<classmethod({C.foo!r})>')
 
     def test_unsortable(self):
         # Repr.repr() used to call sorted() on sets, frozensets and dicts