diff -r e245b0d7209b Lib/test/test_gc.py
--- a/Lib/test/test_gc.py	Sun Oct 20 02:01:29 2013 -0700
+++ b/Lib/test/test_gc.py	Fri Nov 08 13:25:29 2013 +0100
@@ -127,10 +127,16 @@
         del a
         self.assertNotEqual(gc.collect(), 0)
         del B, C
-        self.assertNotEqual(gc.collect(), 0)
+        if hasattr(sys, 'getcounts'):
+            self.assertEqual(gc.collect(), 0)
+        else:
+            self.assertNotEqual(gc.collect(), 0)
         A.a = A()
         del A
-        self.assertNotEqual(gc.collect(), 0)
+        if hasattr(sys, 'getcounts'):
+            self.assertEqual(gc.collect(), 0)
+        else:
+            self.assertNotEqual(gc.collect(), 0)
         self.assertEqual(gc.collect(), 0)
 
     def test_method(self):
@@ -618,6 +624,8 @@
         stderr = run_command(code % "gc.DEBUG_SAVEALL")
         self.assertNotIn(b"uncollectable objects at shutdown", stderr)
 
+    @unittest.skipIf(hasattr(sys, 'getcounts'),
+                     'types are immortal if COUNT_ALLOCS is used')
     def test_gc_main_module_at_shutdown(self):
         # Create a reference cycle through the __main__ module and check
         # it gets collected at interpreter shutdown.
@@ -632,6 +640,8 @@
         rc, out, err = assert_python_ok('-c', code)
         self.assertEqual(out.strip(), b'__del__ called')
 
+    @unittest.skipIf(hasattr(sys, 'getcounts'),
+                     'types are immortal if COUNT_ALLOCS is used')
     def test_gc_ordinary_module_at_shutdown(self):
         # Same as above, but with a non-__main__ module.
         with temp_dir() as script_dir:
diff -r e245b0d7209b Lib/test/test_module.py
--- a/Lib/test/test_module.py	Sun Oct 20 02:01:29 2013 -0700
+++ b/Lib/test/test_module.py	Fri Nov 08 13:25:29 2013 +0100
@@ -81,6 +81,8 @@
         gc_collect()
         self.assertEqual(f().__dict__["bar"], 4)
 
+    @unittest.skipIf(hasattr(sys, 'getcounts'), 
+                     'types are immortal if COUNT_ALLOCS is used')
     def test_clear_dict_in_ref_cycle(self):
         destroyed = []
         m = ModuleType("foo")
@@ -96,6 +98,8 @@
         gc_collect()
         self.assertEqual(destroyed, [1])
 
+    @unittest.skipIf(hasattr(sys, 'getcounts'), 
+                     'types are immortal if COUNT_ALLOCS is used')
     def test_weakref(self):
         m = ModuleType("foo")
         wr = weakref.ref(m)
@@ -190,6 +194,8 @@
         self.assertEqual(r[:25], "<module 'unittest' from '")
         self.assertEqual(r[-13:], "__init__.py'>")
 
+    @unittest.skipIf(hasattr(sys, 'getcounts'),
+                     'skipping since COUNT_ALLOCS was used, see issue19527')
     def test_module_finalization_at_shutdown(self):
         # Module globals and builtins should still be available during shutdown
         rc, out, err = assert_python_ok("-c", "from test import final_a")