diff --git a/swh/storage/tests/test_api_client.py b/swh/storage/tests/test_api_client.py
--- a/swh/storage/tests/test_api_client.py
+++ b/swh/storage/tests/test_api_client.py
@@ -10,11 +10,12 @@
 from swh.core.tests.server_testing import ServerTestFixture
 from swh.storage.api.client import RemoteStorage
 from swh.storage.api.server import app
-from swh.storage.tests.test_storage import CommonTestStorage
+from swh.storage.tests.test_storage import CommonTestStorage, \
+                                           StorageTestDbFixture
 
 
 class TestRemoteStorage(CommonTestStorage, ServerTestFixture,
-                        unittest.TestCase):
+                        StorageTestDbFixture, unittest.TestCase):
     """Test the remote storage API.
 
     This class doesn't define any tests as we want identical
diff --git a/swh/storage/tests/test_storage.py b/swh/storage/tests/test_storage.py
--- a/swh/storage/tests/test_storage.py
+++ b/swh/storage/tests/test_storage.py
@@ -19,7 +19,7 @@
 
 
 @pytest.mark.db
-class BaseTestStorage(StorageTestFixture):
+class StorageTestDbFixture(StorageTestFixture):
     def setUp(self):
         super().setUp()
 
@@ -29,6 +29,15 @@
 
         self.maxDiff = None
 
+    def tearDown(self):
+        self.reset_storage_tables()
+        super().tearDown()
+
+
+class TestStorageData:
+    def setUp(self):
+        super().setUp()
+
         self.cont = {
             'data': b'42\n',
             'length': 3,
@@ -509,12 +518,8 @@
             'next_branch': None
         }
 
-    def tearDown(self):
-        self.reset_storage_tables()
-        super().tearDown()
-
 
-class CommonTestStorage(BaseTestStorage):
+class CommonTestStorage(TestStorageData):
     """Base class for Storage testing.
 
     This class is used as-is to test local storage (see TestLocalStorage
@@ -1842,7 +1847,8 @@
         self.assertIsNotNone(o_m1)
 
 
-class TestLocalStorage(CommonTestStorage, unittest.TestCase):
+class TestLocalStorage(CommonTestStorage, StorageTestDbFixture,
+                       unittest.TestCase):
     """Test the local storage"""
 
     # Can only be tested with local storage as you can't mock
@@ -1921,7 +1927,8 @@
         self.assertEqual(missing, [self.cont['sha1']])
 
 
-class AlteringSchemaTest(BaseTestStorage, unittest.TestCase):
+class AlteringSchemaTest(TestStorageData, StorageTestDbFixture,
+                         unittest.TestCase):
     """This class is dedicated for the rare case where the schema needs to
        be altered dynamically.