diff --git a/swh/objstorage/tests/objstorage_testing.py b/swh/objstorage/tests/objstorage_testing.py
--- a/swh/objstorage/tests/objstorage_testing.py
+++ b/swh/objstorage/tests/objstorage_testing.py
@@ -4,15 +4,13 @@
 # See top-level LICENSE file for more information
 
 import time
+import collections
 
 from swh.objstorage import exc
 from swh.objstorage.objstorage import compute_hash
 
 
-class ObjStorageTestFixture():
-
-    def setUp(self):
-        super().setUp()
+class ObjStorageTestFixture:
 
     def hash_content(self, content):
         obj_id = compute_hash(content)
@@ -116,7 +114,7 @@
         content, obj_id = self.hash_content(b'content_to_delete')
         self.storage.add(content, obj_id=obj_id)
         with self.assertRaises(PermissionError):
-            self.assertTrue(self.storage.delete(obj_id))
+            self.storage.delete(obj_id)
 
     def test_delete_not_allowed_by_default(self):
         content, obj_id = self.hash_content(b'content_to_delete')
@@ -137,24 +135,29 @@
         def gen_content():
             yield b'chunk1'
             time.sleep(0.5)
-            yield b'chunk2'
+            yield b'chunk42'
         _, obj_id = self.hash_content(b'placeholder_id')
         try:
             self.storage.add_stream(gen_content(), obj_id=obj_id)
         except NotImplementedError:
             return
-        self.assertContentMatch(obj_id, b'chunk1chunk2')
+        self.assertContentMatch(obj_id, b'chunk1chunk42')
 
     def test_get_stream(self):
-        content_l = [b'1', b'2', b'3', b'4', b'5', b'6', b'7', b'8', b'9']
-        content = b''.join(content_l)
+        content = b'123456789'
         _, obj_id = self.hash_content(content)
         self.storage.add(content, obj_id=obj_id)
+        r = self.storage.get(obj_id)
+        self.assertEqual(r, content)
+
         try:
-            r = list(self.storage.get_stream(obj_id, chunk_size=1))
+            r = self.storage.get_stream(obj_id, chunk_size=1)
         except NotImplementedError:
             return
-        self.assertEqual(r, content_l)
+        self.assertTrue(isinstance(r, collections.Iterator))
+        r = list(r)
+        self.assertEqual(len(r), 9)
+        self.assertEqual(b''.join(r), content)
 
     def test_add_batch(self):
         contents = {}
diff --git a/swh/objstorage/tests/test_objstorage_api.py b/swh/objstorage/tests/test_objstorage_api.py
--- a/swh/objstorage/tests/test_objstorage_api.py
+++ b/swh/objstorage/tests/test_objstorage_api.py
@@ -41,3 +41,9 @@
     def tearDown(self):
         super().tearDown()
         shutil.rmtree(self.tmpdir)
+
+    def test_delete_not_allowed(self):
+        self.skipTest('makes no sense to test this for the remote api')
+
+    def test_delete_not_allowed_by_default(self):
+        self.skipTest('makes no sense to test this for the remote api')