diff -r a12da014d394 Lib/_collections_abc.py
--- a/Lib/_collections_abc.py	Mon Jan 05 14:39:06 2015 -0600
+++ b/Lib/_collections_abc.py	Mon Jan 05 17:51:37 2015 -0600
@@ -661,13 +661,18 @@
         for i in reversed(range(len(self))):
             yield self[i]
 
-    def index(self, value):
-        '''S.index(value) -> integer -- return first index of value.
+    def index(self, value, start=0, stop=None):
+        '''S.index(value, [start, [stop]]) -> integer -- return first index of value.
            Raises ValueError if the value is not present.
         '''
-        for i, v in enumerate(self):
-            if v == value:
-                return i
+        i = start
+        while stop is None or i < stop:
+            try:
+                if self[i] == value:
+                    return i
+            except IndexError:
+                break
+            i += 1
         raise ValueError
 
     def count(self, value):
diff -r a12da014d394 Lib/test/test_collections.py
--- a/Lib/test/test_collections.py	Mon Jan 05 14:39:06 2015 -0600
+++ b/Lib/test/test_collections.py	Mon Jan 05 17:51:37 2015 -0600
@@ -614,9 +614,9 @@
 
 class TestCollectionABCs(ABCTestCase):
 
-    # XXX For now, we only test some virtual inheritance properties.
-    # We should also test the proper behavior of the collection ABCs
-    # as real base classes or mix-in classes.
+    # XXX The virtual inheritance properties are tested here, but we need more
+    # tests for proper behavior of the collection ABCs as real base classes or
+    # mix-in classes.
 
     def test_Set(self):
         for sample in [set, frozenset]:
@@ -1000,6 +1000,28 @@
         self.validate_abstract_methods(Sequence, '__contains__', '__iter__', '__len__',
             '__getitem__')
 
+    def test_Sequence_mixins(self):
+        class SequenceSubclass(Sequence):
+            def __init__(self, seq=()):
+                self.seq = seq
+
+            def __getitem__(self, index):
+                return self.seq[index]
+
+            def __len__(self):
+                return len(self.seq)
+
+        seq = SequenceSubclass('aab')
+        self.assertEqual(seq.index('a'), 0)
+        self.assertEqual(seq.index('a'), 0, 1)
+        self.assertEqual(seq.index('b'), 2)
+        self.assertEqual(seq.index('a', 1), 1)
+        self.assertRaises(ValueError, seq.index, 'a', 2)
+        self.assertRaises(ValueError, seq.index, 'a', 1, 1)
+        self.assertRaises(ValueError, seq.index, 'b', 0, 1)
+
+        # XXX We should test the other mixin methods too.
+
     def test_ByteString(self):
         for sample in [bytes, bytearray]:
             self.assertIsInstance(sample(), ByteString)