diff --git a/zerver/tests/test_delete_unclaimed_attachments.py b/zerver/tests/test_delete_unclaimed_attachments.py
index f076964990..f151d2d667 100644
--- a/zerver/tests/test_delete_unclaimed_attachments.py
+++ b/zerver/tests/test_delete_unclaimed_attachments.py
@@ -26,7 +26,7 @@ class UnclaimedAttachmentTest(UploadSerializeMixin, ZulipTestCase):
             uploader = self.example_user("hamlet")
         self.login_user(uploader)
 
-        with time_machine.travel(when):
+        with time_machine.travel(when, tick=False):
             file_obj = StringIO("zulip!")
             file_obj.name = filename
             response = self.assert_json_success(
diff --git a/zerver/tests/test_invite.py b/zerver/tests/test_invite.py
index bf7ddad00d..e6915a1a24 100644
--- a/zerver/tests/test_invite.py
+++ b/zerver/tests/test_invite.py
@@ -335,7 +335,7 @@ class InviteUserTest(InviteUserBase):
 
         # We've sent 40 invites "today".  Fast-forward 48 hours
         # and ensure that we can invite more people
-        with time_machine.travel(timezone_now() + datetime.timedelta(hours=48)):
+        with time_machine.travel(timezone_now() + datetime.timedelta(hours=48), tick=False):
             result = try_invite(5, default_realm_max=30, new_realm_max=20, realm_max=10)
             self.assert_json_success(result)
             self.check_sent_emails([f"zulip-{i:02}@zulip.com" for i in range(5)], clear=True)