diff --git a/changelog.d/3601.bugfix b/changelog.d/3601.bugfix
new file mode 100644
index 0000000000..1678b261d0
--- /dev/null
+++ b/changelog.d/3601.bugfix
@@ -0,0 +1 @@
+Fix failure to persist events over federation under load
diff --git a/synapse/storage/events.py b/synapse/storage/events.py
index d39796f5ba..200f5ec95f 100644
--- a/synapse/storage/events.py
+++ b/synapse/storage/events.py
@@ -574,11 +574,13 @@ class EventsStore(EventsWorkerStore):
 
         for ev, ctx in events_context:
             if ctx.state_group is None:
-                # I don't think this can happen, but let's double-check
-                raise Exception(
-                    "Context for new extremity event %s has no state "
-                    "group" % (ev.event_id, ),
-                )
+                # This should only happen for outlier events.
+                if not ev.internal_metadata.is_outlier():
+                    raise Exception(
+                        "Context for new event %s has no state "
+                        "group" % (ev.event_id, ),
+                    )
+                continue
 
             if ctx.state_group in state_groups_map:
                 continue
@@ -606,7 +608,7 @@ class EventsStore(EventsWorkerStore):
         for event_id in new_latest_event_ids:
             # First search in the list of new events we're adding.
             for ev, ctx in events_context:
-                if event_id == ev.event_id:
+                if event_id == ev.event_id and ctx.state_group is not None:
                     event_id_to_state_group[event_id] = ctx.state_group
                     break
             else: