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
@@ -67,7 +67,7 @@
 
 
 class TestStorage:
-    """Base class for Storage testing.
+    """Main class for Storage testing.
 
     This class is used as-is to test local storage (see TestLocalStorage
     below) and remote storage (see TestRemoteStorage in
@@ -2919,8 +2919,7 @@
         assert m_by_provider == expected_results
 
 
-class TestStorageCommonProp:
-    _test_origin_ids = True
+class TestStorageGeneratedData:
 
     def assert_contents_ok(self, expected_contents, actual_contents,
                            keys_to_check={'sha1', 'data'}):