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
@@ -11,7 +11,6 @@
 from collections import defaultdict
 from unittest.mock import Mock, patch
 
-import psycopg2.errors
 import pytest
 
 from hypothesis import given, strategies, settings, HealthCheck
@@ -594,7 +593,9 @@
         self.assertEqual(journal_objects,
                          [('content', expected_cont)])
 
+    @pytest.mark.db
     def test_content_add_validation(self):
+        import psycopg2.errors
         cont = self.cont
 
         with self.assertRaisesRegex(ValueError, 'status'):
@@ -1007,7 +1008,9 @@
         after_missing = list(self.storage.directory_missing([self.dir['id']]))
         self.assertEqual([], after_missing)
 
+    @pytest.mark.db
     def test_directory_add_validation(self):
+        import psycopg2.errors
         dir_ = copy.deepcopy(self.dir)
         dir_['entries'][0]['type'] = 'foobar'
 
@@ -1173,7 +1176,9 @@
         actual_result = self.storage.revision_add([self.revision])
         self.assertEqual(actual_result, {'revision:add': 0})
 
+    @pytest.mark.db
     def test_revision_add_validation(self):
+        import psycopg2.errors
         rev = copy.deepcopy(self.revision)
         rev['date']['offset'] = 2**16
 
@@ -1355,7 +1360,9 @@
         self.assertEqual(list(self.journal_writer.objects),
                          [('release', release)])
 
+    @pytest.mark.db
     def test_release_add_validation(self):
+        import psycopg2.errors
         rel = copy.deepcopy(self.release)
         rel['date']['offset'] = 2**16
 
@@ -1769,7 +1776,9 @@
                           ('origin_visit', data1),
                           ('origin_visit', data2)])
 
+    @pytest.mark.db
     def test_origin_visit_add_validation(self):
+        import psycopg2.errors
         origin_id_or_url = self.storage.origin_add_one(self.origin2)
 
         with self.assertRaises((TypeError, psycopg2.errors.UndefinedFunction)):
@@ -1931,7 +1940,9 @@
                           ('origin_visit', data4),
                           ('origin_visit', data5)])
 
+    @pytest.mark.db
     def test_origin_visit_update_validation(self):
+        import psycopg2.errors
         origin_id = self.storage.origin_add_one(self.origin)
         visit = self.storage.origin_visit_add(
             origin_id,