diff --git a/gnocchi/tests/base.py b/gnocchi/tests/base.py
index e5412981..0388d1ed 100644
--- a/gnocchi/tests/base.py
+++ b/gnocchi/tests/base.py
@@ -294,6 +294,11 @@ class TestCase(base.BaseTestCase):
                 os.getenv("CEPH_CONF"), pool_name), shell=True)
             self.conf.set_override('ceph_pool', pool_name, 'storage')
 
+        # Override the bucket prefix to be unique to avoid concurrent access
+        # with any other test
+        self.conf.set_override("s3_bucket_prefix", str(uuid.uuid4())[:26],
+                               "storage")
+
         self.storage = storage.get_driver(self.conf)
         # NOTE(jd) Do not upgrade the storage. We don't really need the storage
         # upgrade for now, and the code that upgrade from pre-1.3
diff --git a/gnocchi/tests/test_storage.py b/gnocchi/tests/test_storage.py
index eb55e839..6fc8f9e9 100644
--- a/gnocchi/tests/test_storage.py
+++ b/gnocchi/tests/test_storage.py
@@ -55,10 +55,6 @@ class TestStorageDriver(tests_base.TestCase):
     def test_corrupted_data(self):
         if not isinstance(self.storage, _carbonara.CarbonaraBasedStorage):
             self.skipTest("This driver is not based on Carbonara")
-        if self.conf.storage.driver == "s3":
-            self.skipTest(
-                "This test does not work with S3 as backend as the S3 driver "
-                "has no fake client, and tests run in parallel.")
 
         self.storage.incoming.add_measures(self.metric, [
             storage.Measure(utils.dt_to_unix_ns(2014, 1, 1, 12, 0, 1), 69),
@@ -81,10 +77,6 @@ class TestStorageDriver(tests_base.TestCase):
         self.assertIn((utils.datetime_utc(2014, 1, 1, 13), 300.0, 1), m)
 
     def test_list_metric_with_measures_to_process(self):
-        if self.conf.storage.driver == "s3":
-            self.skipTest(
-                "This test does not work with S3 as backend as the S3 driver "
-                "has no fake client, and tests run in parallel.")
         metrics = self.storage.incoming.list_metric_with_measures_to_process(
             None, None, full=True)
         self.assertEqual(set(), metrics)
@@ -150,10 +142,6 @@ class TestStorageDriver(tests_base.TestCase):
 
     @mock.patch('gnocchi.carbonara.SplitKey.POINTS_PER_SPLIT', 48)
     def test_add_measures_update_subset_split(self):
-        if self.conf.storage.driver == "s3":
-            self.skipTest(
-                "This test does not work with S3 as backend as the S3 driver "
-                "has no fake client, and tests run in parallel.")
         m, m_sql = self._create_metric('medium')
         measures = [
             storage.Measure(utils.dt_to_unix_ns(2014, 1, 6, i, j, 0), 100)
@@ -177,10 +165,6 @@ class TestStorageDriver(tests_base.TestCase):
         self.assertEqual(1, count)
 
     def test_add_measures_update_subset(self):
-        if self.conf.storage.driver == "s3":
-            self.skipTest(
-                "This test does not work with S3 as backend as the S3 driver "
-                "has no fake client, and tests run in parallel.")
         m, m_sql = self._create_metric('medium')
         measures = [
             storage.Measure(utils.dt_to_unix_ns(2014, 1, 6, i, j, 0), 100)