diff --git a/Lib/test/test_bytes.py b/Lib/test/test_bytes.py
index c368143..c4a3e51 100644
--- a/Lib/test/test_bytes.py
+++ b/Lib/test/test_bytes.py
@@ -397,7 +397,7 @@
         self.assertEqual(b.rpartition(b'i'), (b'mississipp', b'i', b''))
 
     def test_pickling(self):
-        for proto in range(pickle.HIGHEST_PROTOCOL):
+        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
             for b in b"", b"a", b"abc", b"\xffab\x80", b"\0\0\377\0\0":
                 b = self.type2test(b)
                 ps = pickle.dumps(b, proto)
@@ -979,7 +979,7 @@
         a = ByteArraySubclass(b"abcd")
         a.x = 10
         a.y = ByteArraySubclass(b"efgh")
-        for proto in range(pickle.HIGHEST_PROTOCOL):
+        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
             b = pickle.loads(pickle.dumps(a, proto))
             self.assertNotEqual(id(a), id(b))
             self.assertEqual(a, b)
diff --git a/Lib/test/test_range.py b/Lib/test/test_range.py
index b14a22b..43fadf0 100644
--- a/Lib/test/test_range.py
+++ b/Lib/test/test_range.py
@@ -65,7 +65,7 @@
     def test_pickling(self):
         testcases = [(13,), (0, 11), (-22, 10), (20, 3, -1),
                      (13, 21, 3), (-2, 2, 2)]
-        for proto in range(pickle.HIGHEST_PROTOCOL):
+        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
             for t in testcases:
                 r = range(*t)
                 self.assertEquals(list(pickle.loads(pickle.dumps(r, proto))),