diff --git a/synapse/storage/databases/main/stream.py b/synapse/storage/databases/main/stream.py
index 9ae1fe6c15..9e94cb08f6 100644
--- a/synapse/storage/databases/main/stream.py
+++ b/synapse/storage/databases/main/stream.py
@@ -412,6 +412,43 @@ def _filter_results(
     return True
 
 
+def _filter_results_by_stream(
+    lower_token: Optional[RoomStreamToken],
+    upper_token: Optional[RoomStreamToken],
+    instance_name: str,
+    stream_ordering: int,
+) -> bool:
+    """
+    This function only works with "live" tokens with `stream_ordering` only. See
+    `_filter_results(...)` if you want to work with all tokens.
+
+    Returns True if the event persisted by the given instance at the given
+    stream_ordering falls between the two tokens (taking a None
+    token to mean unbounded).
+
+    Used to filter results from fetching events in the DB against the given
+    tokens. This is necessary to handle the case where the tokens include
+    position maps, which we handle by fetching more than necessary from the DB
+    and then filtering (rather than attempting to construct a complicated SQL
+    query).
+    """
+    if lower_token:
+        assert lower_token.topological is None
+
+        # If these are live tokens we compare the stream ordering against the
+        # writers stream position.
+        if stream_ordering <= lower_token.get_stream_pos_for_instance(instance_name):
+            return False
+
+    if upper_token:
+        assert upper_token.topological is None
+
+        if upper_token.get_stream_pos_for_instance(instance_name) < stream_ordering:
+            return False
+
+    return True
+
+
 def filter_to_clause(event_filter: Optional[Filter]) -> Tuple[str, List[str]]:
     # NB: This may create SQL clauses that don't optimise well (and we don't
     # have indices on all possible clauses). E.g. it may create
@@ -764,6 +801,8 @@ class StreamWorkerStore(EventsWorkerStore, SQLBaseStore):
         Fetch membership events (and the previous event that was replaced by that one)
         for a given user.
 
+        Note: This function only works with "live" tokens with `stream_ordering` only.
+
         We're looking for membership changes in the token range (> `from_key` and <=
         `to_key`).
 
@@ -837,7 +876,6 @@ class StreamWorkerStore(EventsWorkerStore, SQLBaseStore):
                     s.room_id,
                     COALESCE(e.instance_name, s.instance_name),
                     COALESCE(e.stream_ordering, s.stream_id),
-                    e.topological_ordering,
                     m.membership,
                     e.sender
                 FROM current_state_delta_stream AS s
@@ -859,7 +897,6 @@ class StreamWorkerStore(EventsWorkerStore, SQLBaseStore):
                 room_id,
                 instance_name,
                 stream_ordering,
-                topological_ordering,
                 membership,
                 sender,
             ) in txn:
@@ -867,12 +904,10 @@ class StreamWorkerStore(EventsWorkerStore, SQLBaseStore):
                 assert instance_name is not None
                 assert stream_ordering is not None
 
-                if _filter_results(
+                if _filter_results_by_stream(
                     from_key,
                     to_key,
                     instance_name,
-                    # TODO: This isn't always filled now
-                    topological_ordering,
                     stream_ordering,
                 ):
                     # When the server leaves a room, it will insert new rows with