diff --git a/changelog.d/6652.bugfix b/changelog.d/6652.bugfix
new file mode 100644
index 000000000..7e9781d65
--- /dev/null
+++ b/changelog.d/6652.bugfix
@@ -0,0 +1 @@
+Fix a bug causing Synapse not to fetch missing events when it believes it has every event in the room.
diff --git a/synapse/handlers/federation.py b/synapse/handlers/federation.py
index 72a0febc2..61b6713c8 100644
--- a/synapse/handlers/federation.py
+++ b/synapse/handlers/federation.py
@@ -248,13 +248,13 @@ class FederationHandler(BaseHandler):
             prevs = set(pdu.prev_event_ids())
             seen = await self.store.have_seen_events(prevs)
 
-            if min_depth and pdu.depth < min_depth:
+            if min_depth is not None and pdu.depth < min_depth:
                 # This is so that we don't notify the user about this
                 # message, to work around the fact that some events will
                 # reference really really old events we really don't want to
                 # send to the clients.
                 pdu.internal_metadata.outlier = True
-            elif min_depth and pdu.depth > min_depth:
+            elif min_depth is not None and pdu.depth > min_depth:
                 missing_prevs = prevs - seen
                 if sent_to_us_directly and missing_prevs:
                     # If we're missing stuff, ensure we only fetch stuff one
diff --git a/synapse/storage/data_stores/main/event_federation.py b/synapse/storage/data_stores/main/event_federation.py
index 5cb8cd96d..60c67457b 100644
--- a/synapse/storage/data_stores/main/event_federation.py
+++ b/synapse/storage/data_stores/main/event_federation.py
@@ -470,7 +470,7 @@ class EventFederationStore(EventFederationWorkerStore):
     def _update_min_depth_for_room_txn(self, txn, room_id, depth):
         min_depth = self._get_min_depth_interaction(txn, room_id)
 
-        if min_depth and depth >= min_depth:
+        if min_depth is not None and depth >= min_depth:
             return
 
         self.db.simple_upsert_txn(