diff --git a/Lib/test/datetimetester.py b/Lib/test/datetimetester.py
index bccd97a..b25e6c1 100644
--- a/Lib/test/datetimetester.py
+++ b/Lib/test/datetimetester.py
@@ -61,8 +61,9 @@
         self.assertEqual(datetime.MAXYEAR, 9999)
 
     def test_name_cleanup(self):
-        if '_Fast' not in str(self):
-            return
+        if '_Pure' in self.__class__.__name__:
+            self.skipTest('Only run for Fast C implementation')
+
         datetime = datetime_module
         names = set(name for name in dir(datetime)
                     if not name.startswith('__') and not name.endswith('__'))
@@ -72,8 +73,9 @@
         self.assertEqual(names - allowed, set([]))
 
     def test_divide_and_round(self):
-        if '_Fast' in str(self):
-            return
+        if '_Fast' in self.__class__.__name__:
+            self.skipTest('Only run for Pure Python implementation')
+
         dar = datetime_module._divide_and_round
 
         self.assertEqual(dar(-10, -3), 3)
@@ -2851,7 +2853,7 @@
         self.assertRaises(TypeError, t.strftime, "%Z")
 
         # Issue #6697:
-        if '_Fast' in str(self):
+        if '_Fast' in self.__class__.__name__:
             Badtzname.tz = '\ud800'
             self.assertRaises(ValueError, t.strftime, "%Z")
 
diff --git a/Lib/test/test_datetime.py b/Lib/test/test_datetime.py
index 242e1bb..2d00b56 100644
--- a/Lib/test/test_datetime.py
+++ b/Lib/test/test_datetime.py
@@ -20,7 +20,7 @@
 # XXX(gb) First run all the _Pure tests, then all the _Fast tests.  You might
 # not believe this, but in spite of all the sys.modules trickery running a _Pure
 # test last will leave a mix of pure and native datetime stuff lying around.
-test_classes = []
+all_test_classes = []
 
 for module, suffix in zip(test_modules, test_suffixes):
     test_classes = []
@@ -33,7 +33,8 @@
             suit = cls()
             test_classes.extend(type(test) for test in suit)
     for cls in test_classes:
-        cls.__name__ = name + suffix
+        cls.__name__ += suffix
+        cls.__qualname__ += suffix
         @classmethod
         def setUpClass(cls_, module=module):
             cls_._save_sys_modules = sys.modules.copy()
@@ -46,9 +47,10 @@
             sys.modules.update(cls_._save_sys_modules)
         cls.setUpClass = setUpClass
         cls.tearDownClass = tearDownClass
+    all_test_classes.extend(test_classes)
 
 def test_main():
-    run_unittest(*test_classes)
+    run_unittest(*all_test_classes)
 
 if __name__ == "__main__":
     test_main()