diff --git a/test/unit/common/test_db_replicator.py b/test/unit/common/test_db_replicator.py
index bf0cbeeacd..726ed79e1c 100644
--- a/test/unit/common/test_db_replicator.py
+++ b/test/unit/common/test_db_replicator.py
@@ -1171,10 +1171,10 @@ class TestDBReplicator(unittest.TestCase):
         db_file = __file__
         replicator = TestReplicator({})
         replicator._http_connect(node, partition, db_file)
-        db_replicator.ReplConnection.assert_has_calls(
+        db_replicator.ReplConnection.assert_has_calls([
             mock.call(node, partition,
                       os.path.basename(db_file).split('.', 1)[0],
-                      replicator.logger))
+                      replicator.logger)])
 
 
 class TestReplToNode(unittest.TestCase):
diff --git a/test/unit/common/test_wsgi.py b/test/unit/common/test_wsgi.py
index 67142decdd..f6a5818b74 100644
--- a/test/unit/common/test_wsgi.py
+++ b/test/unit/common/test_wsgi.py
@@ -354,7 +354,7 @@ class TestWSGI(unittest.TestCase):
         _eventlet.patcher.monkey_patch.assert_called_with(all=False,
                                                           socket=True)
         _eventlet.debug.hub_exceptions.assert_called_with(False)
-        _wsgi.server.assert_called()
+        self.assertTrue(_wsgi.server.called)
         args, kwargs = _wsgi.server.call_args
         server_sock, server_app, server_logger = args
         self.assertEquals(sock, server_sock)
@@ -397,7 +397,7 @@ class TestWSGI(unittest.TestCase):
                 sock = listen(('localhost', 0))
                 wsgi.run_server(conf, logger, sock)
 
-        _wsgi.server.assert_called()
+        self.assertTrue(_wsgi.server.called)
         args, kwargs = _wsgi.server.call_args
         self.assertEquals(kwargs.get('capitalize_response_headers'), False)
 
@@ -442,7 +442,7 @@ class TestWSGI(unittest.TestCase):
         _eventlet.patcher.monkey_patch.assert_called_with(all=False,
                                                           socket=True)
         _eventlet.debug.hub_exceptions.assert_called_with(False)
-        _wsgi.server.assert_called()
+        self.assertTrue(_wsgi.server.called)
         args, kwargs = _wsgi.server.call_args
         server_sock, server_app, server_logger = args
         self.assertEquals(sock, server_sock)
@@ -493,7 +493,7 @@ class TestWSGI(unittest.TestCase):
         _eventlet.patcher.monkey_patch.assert_called_with(all=False,
                                                           socket=True)
         _eventlet.debug.hub_exceptions.assert_called_with(True)
-        mock_server.assert_called()
+        self.assertTrue(mock_server.called)
         args, kwargs = mock_server.call_args
         server_sock, server_app, server_logger = args
         self.assertEquals(sock, server_sock)
diff --git a/test/unit/obj/test_expirer.py b/test/unit/obj/test_expirer.py
index 19a84f29b9..ca246dbeb0 100644
--- a/test/unit/obj/test_expirer.py
+++ b/test/unit/obj/test_expirer.py
@@ -718,7 +718,7 @@ class TestObjectExpirer(TestCase):
         x = expirer.ObjectExpirer({})
         x.swift.make_request = mock.MagicMock()
         x.delete_actual_object(name, timestamp)
-        x.swift.make_request.assert_called_once()
+        self.assertEqual(x.swift.make_request.call_count, 1)
         self.assertEqual(x.swift.make_request.call_args[0][1],
                          '/v1/' + urllib.quote(name))