diff -r 6907716e7ccb Lib/rlcompleter.py
--- a/Lib/rlcompleter.py	Tue Sep 08 05:53:42 2015 +0300
+++ b/Lib/rlcompleter.py	Tue Sep 08 06:04:28 2015 +0300
@@ -136,20 +136,35 @@ class Completer:
             return []
 
         # get the content of the object, except __builtins__
-        words = dir(thisobject)
-        if "__builtins__" in words:
-            words.remove("__builtins__")
+        words = set(dir(thisobject))
+        words.discard("__builtins__")
 
         if hasattr(thisobject, '__class__'):
-            words.append('__class__')
-            words.extend(get_class_members(thisobject.__class__))
+            words.add('__class__')
+            words.update(get_class_members(thisobject.__class__))
         matches = []
         n = len(attr)
-        for word in words:
-            if word[:n] == attr and hasattr(thisobject, word):
-                val = getattr(thisobject, word)
-                word = self._callable_postfix(val, "%s.%s" % (expr, word))
-                matches.append(word)
+        if attr == '':
+            noprefix = '_'
+        elif attr == '_':
+            noprefix = '__'
+        else:
+            noprefix = None
+        while True:
+            for word in words:
+                if (word[:n] == attr and
+                    not (noprefix and word[:n+1] == noprefix) and
+                    hasattr(thisobject, word)):
+                    val = getattr(thisobject, word)
+                    word = self._callable_postfix(val, "%s.%s" % (expr, word))
+                    matches.append(word)
+            if matches or not noprefix:
+                break
+            if noprefix == '_':
+                noprefix = '__'
+            else:
+                noprefix = None
+        matches.sort()
         return matches
 
 def get_class_members(klass):
diff -r 6907716e7ccb Lib/test/test_rlcompleter.py
--- a/Lib/test/test_rlcompleter.py	Tue Sep 08 05:53:42 2015 +0300
+++ b/Lib/test/test_rlcompleter.py	Tue Sep 08 06:04:28 2015 +0300
@@ -5,6 +5,7 @@ import rlcompleter
 class CompleteMe:
     """ Trivial class used in testing rlcompleter.Completer. """
     spam = 1
+    _ham = 2
 
 
 class TestRlcompleter(unittest.TestCase):
@@ -51,11 +52,25 @@ class TestRlcompleter(unittest.TestCase)
                          ['str.{}('.format(x) for x in dir(str)
                           if x.startswith('s')])
         self.assertEqual(self.stdcompleter.attr_matches('tuple.foospamegg'), [])
+        expected = sorted({'None.%s%s' % (x, '(' if x != '__doc__' else '')
+                           for x in dir(None)})
+        self.assertEqual(self.stdcompleter.attr_matches('None.'), expected)
+        self.assertEqual(self.stdcompleter.attr_matches('None._'), expected)
+        self.assertEqual(self.stdcompleter.attr_matches('None.__'), expected)
 
         # test with a customized namespace
         self.assertEqual(self.completer.attr_matches('CompleteMe.sp'),
                          ['CompleteMe.spam'])
         self.assertEqual(self.completer.attr_matches('Completeme.egg'), [])
+        self.assertEqual(self.completer.attr_matches('CompleteMe.'),
+                         ['CompleteMe.mro(', 'CompleteMe.spam'])
+        self.assertEqual(self.completer.attr_matches('CompleteMe._'),
+                         ['CompleteMe._ham'])
+        matches = self.completer.attr_matches('CompleteMe.__')
+        for x in matches:
+            self.assertTrue(x.startswith('CompleteMe.__'), x)
+        self.assertIn('CompleteMe.__name__', matches)
+        self.assertIn('CompleteMe.__new__(', matches)
 
         CompleteMe.me = CompleteMe
         self.assertEqual(self.completer.attr_matches('CompleteMe.me.me.sp'),