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 +11,7 @@
 from collections import defaultdict
 from unittest.mock import Mock, patch
 
-import psycopg2.errors
+import psycopg2
 import pytest
 
 from hypothesis import given, strategies, settings, HealthCheck
@@ -604,8 +604,7 @@
             self.storage.content_add([{**cont, 'length': -2}])
 
         with self.assertRaisesRegex(
-                (ValueError, psycopg2.errors.NotNullViolation),
-                "reason"):
+                (ValueError, psycopg2.IntegrityError), 'reason'):
             self.storage.content_add([{**cont, 'status': 'absent'}])
 
         with self.assertRaisesRegex(
@@ -1018,7 +1017,7 @@
         del dir_['entries'][0]['target']
 
         with self.assertRaisesRegex(
-                (TypeError, psycopg2.errors.NotNullViolation), 'target'):
+                (TypeError, psycopg2.IntegrityError), 'target'):
             self.storage.directory_add([dir_])
 
     def test_directory_get_recursive(self):
@@ -1178,24 +1177,21 @@
         rev['date']['offset'] = 2**16
 
         with self.assertRaisesRegex(
-                (ValueError, psycopg2.errors.NumericValueOutOfRange),
-                'offset'):
+                (ValueError, psycopg2.DataError), 'offset'):
             self.storage.revision_add([rev])
 
         rev = copy.deepcopy(self.revision)
         rev['committer_date']['offset'] = 2**16
 
         with self.assertRaisesRegex(
-                (ValueError, psycopg2.errors.NumericValueOutOfRange),
-                'offset'):
+                (ValueError, psycopg2.DataError), 'offset'):
             self.storage.revision_add([rev])
 
         rev = copy.deepcopy(self.revision)
         rev['type'] = 'foobar'
 
         with self.assertRaisesRegex(
-                (ValueError, psycopg2.errors.InvalidTextRepresentation),
-                '(?i)type'):
+                (ValueError, psycopg2.DataError), '(?i)type'):
             self.storage.revision_add([rev])
 
     def test_revision_add_name_clash(self):
@@ -1360,16 +1356,14 @@
         rel['date']['offset'] = 2**16
 
         with self.assertRaisesRegex(
-                (ValueError, psycopg2.errors.NumericValueOutOfRange),
-                'offset'):
+                (ValueError, psycopg2.DataError), 'offset'):
             self.storage.release_add([rel])
 
         rel = copy.deepcopy(self.release)
         rel['author'] = None
 
         with self.assertRaisesRegex(
-                (ValueError, psycopg2.errors.CheckViolation),
-                'date'):
+                (ValueError, psycopg2.IntegrityError), 'date'):
             self.storage.release_add([rel])
 
     def test_release_add_name_clash(self):
@@ -1772,7 +1766,7 @@
     def test_origin_visit_add_validation(self):
         origin_id_or_url = self.storage.origin_add_one(self.origin2)
 
-        with self.assertRaises((TypeError, psycopg2.errors.UndefinedFunction)):
+        with self.assertRaises((TypeError, psycopg2.ProgrammingError)):
             self.storage.origin_visit_add(origin_id_or_url, date=[b'foo'])
 
     @given(strategies.booleans())
@@ -1938,8 +1932,7 @@
             date=self.date_visit2)
 
         with self.assertRaisesRegexp(
-                (ValueError, psycopg2.errors.InvalidTextRepresentation),
-                'status'):
+                (ValueError, psycopg2.DataError), 'status'):
             self.storage.origin_visit_update(
                 origin_id, visit['visit'], status='foobar')