diff --git a/tests/handlers/test_sync.py b/tests/handlers/test_sync.py
index 18ec2ca6b6..21525c4a98 100644
--- a/tests/handlers/test_sync.py
+++ b/tests/handlers/test_sync.py
@@ -51,6 +51,7 @@ from synapse.types import (
     create_requester,
 )
 from synapse.util.clock import Clock
+from synapse.util.duration import Duration
 
 import tests.unittest
 import tests.utils
@@ -1058,13 +1059,22 @@ class SyncTestCase(tests.unittest.HomeserverTestCase):
         )
 
         # This should block waiting for the presence stream to update
-        self.pump()
+        #
+        # Advance time a little bit to make the
+        # `wait_for_stream_token(...)` sleep loop iterate.
+        self.reactor.advance(Duration(seconds=2).as_secs())
+        # It should still not be done yet
         self.assertFalse(sync_d.called)
 
         # Marking the stream ID as persisted should unblock the request.
         self.get_success(ctx_mgr.__aexit__(None, None, None))
 
-        self.get_success(sync_d, by=1.0)
+        # Advance time to make another iteration of `wait_for_stream_token(...)` sleep
+        # loop so it sees that we're finally caught up now.
+        self.reactor.advance(Duration(seconds=1).as_secs())
+
+        # Done waiting
+        self.get_success(sync_d)
 
     @parameterized.expand(
         [(key,) for key in StreamKeyType.__members__.values()],
diff --git a/tests/test_notifier.py b/tests/test_notifier.py
index 42ff76eab9..63ec640464 100644
--- a/tests/test_notifier.py
+++ b/tests/test_notifier.py
@@ -137,9 +137,10 @@ class NotifierTestCase(tests.unittest.HomeserverTestCase):
     def test_wait_for_multi_writer_stream_token_with_invalid_future_sync_token(
         self,
     ) -> None:
-        """Like the previous test, except we give a token that has a stream
-        position ahead of what is in the DB, i.e. its invalid and we shouldn't
-        wait for the stream to advance (as it may never do so).
+        """
+        Like `test_wait_for_multi_writer_stream_token_with_future_sync_token`, except we
+        give a token that has a stream position ahead of what is in the DB, i.e. its
+        invalid and we shouldn't wait for the stream to advance (as it may never do so).
 
         This can happen due to older versions of Synapse giving out stream
         positions without persisting them in the DB, and so on restart the