Index: Lib/test/test_exceptions.py
===================================================================
--- Lib/test/test_exceptions.py	(revision 82327)
+++ Lib/test/test_exceptions.py	(working copy)
@@ -3,12 +3,13 @@
 import os
 import sys
 import unittest
-import pickle
 import weakref
 
 from test.support import (TESTFN, unlink, run_unittest, captured_output,
-                          gc_collect)
+                          gc_collect, import_module_implementations)
 
+pickle_implementations = import_module_implementations('pickle')
+
 # XXX This is not really enough, each *operation* should be tested!
 
 class ExceptionTests(unittest.TestCase):
@@ -302,7 +303,7 @@
                                       value, expected[checkArgName]))
 
                 # test for pickling support
-                for p in [pickle]:
+                for p in pickle_implementations:
                     for protocol in range(p.HIGHEST_PROTOCOL + 1):
                         s = p.dumps(e, protocol)
                         new = p.loads(s)
Index: Lib/test/test_set.py
===================================================================
--- Lib/test/test_set.py	(revision 82327)
+++ Lib/test/test_set.py	(working copy)
@@ -4,12 +4,14 @@
 import weakref
 import operator
 import copy
-import pickle
 from random import randrange, shuffle
 import sys
 import warnings
 import collections
 
+pickle_implementations = support.import_module_implementations('pickle')
+
+
 class PassThru(Exception):
     pass
 
@@ -224,15 +226,16 @@
         self.assertFalse(set('cbs').issuperset('a'))
 
     def test_pickling(self):
-        for i in range(pickle.HIGHEST_PROTOCOL + 1):
-            p = pickle.dumps(self.s, i)
-            dup = pickle.loads(p)
-            self.assertEqual(self.s, dup, "%s != %s" % (self.s, dup))
-            if type(self.s) not in (set, frozenset):
-                self.s.x = 10
-                p = pickle.dumps(self.s)
+        for pickle in pickle_implementations:
+            for i in range(pickle.HIGHEST_PROTOCOL + 1):
+                p = pickle.dumps(self.s, i)
                 dup = pickle.loads(p)
-                self.assertEqual(self.s.x, dup.x)
+                self.assertEqual(self.s, dup, "%s != %s" % (self.s, dup))
+                if type(self.s) not in (set, frozenset):
+                    self.s.x = 10
+                    p = pickle.dumps(self.s)
+                    dup = pickle.loads(p)
+                    self.assertEqual(self.s.x, dup.x)
 
     def test_deepcopy(self):
         class Tracer:
@@ -821,10 +824,11 @@
         self.assertEqual(setiter.__length_hint__(), len(self.set))
 
     def test_pickling(self):
-        p = pickle.dumps(self.set)
-        copy = pickle.loads(p)
-        self.assertEqual(self.set, copy,
-                         "%s != %s" % (self.set, copy))
+        for pickle in pickle_implementations:
+            p = pickle.dumps(self.set)
+            copy = pickle.loads(p)
+            self.assertEqual(self.set, copy,
+                             "%s != %s" % (self.set, copy))
 
 #------------------------------------------------------------------------------
 
Index: Lib/test/support.py
===================================================================
--- Lib/test/support.py	(revision 82327)
+++ Lib/test/support.py	(working copy)
@@ -83,6 +83,14 @@
         except ImportError as msg:
             raise unittest.SkipTest(str(msg))
 
+def import_module_implementations(name):
+    """Return a list of one or two modules depending on availability
+    native optimizations.  When optimizations are available, the
+    second module in the returned list will not include them."""
+    result = [importlib.import_module(name)]
+    if ('_' + name) in sys.modules:
+        result.append(import_fresh_module(name, blocked=['_' + name]))
+    return result
 
 def _save_and_remove_module(name, orig_modules):
     """Helper function to save and remove a module from sys.modules
Index: Lib/test/test_collections.py
===================================================================
--- Lib/test/test_collections.py	(revision 82327)
+++ Lib/test/test_collections.py	(working copy)
@@ -17,6 +17,7 @@
 from collections import Sequence, MutableSequence
 from collections import ByteString
 
+pickle_implementations = support.import_module_implementations('pickle')
 TestNT = namedtuple('TestNT', 'x y z')    # type used for pickle tests
 
 class TestNamedTuple(unittest.TestCase):
@@ -165,7 +166,7 @@
 
     def test_pickle(self):
         p = TestNT(x=10, y=20, z=30)
-        for module in (pickle,):
+        for module in pickle_implementations:
             loads = getattr(module, 'loads')
             dumps = getattr(module, 'dumps')
             for protocol in -1, 0, 1, 2: