diff --git a/synapse/handlers/federation.py b/synapse/handlers/federation.py
index ab152e8dcd..4bc4d57efb 100644
--- a/synapse/handlers/federation.py
+++ b/synapse/handlers/federation.py
@@ -2040,8 +2040,10 @@ class FederationHandler(BaseHandler):
             auth_events (dict[(str, str)->synapse.events.EventBase]):
                 Map from (event_type, state_key) to event
 
-                What we expect the event's auth_events to be, based on the event's
-                position in the dag. I think? maybe??
+                Normally, our calculated auth_events based on the state of the room
+                at the event's position in the DAG, though occasionally (eg if the
+                event is an outlier), may be the auth events claimed by the remote
+                server.
 
                 Also NB that this function adds entries to it.
         Returns:
@@ -2091,25 +2093,35 @@ class FederationHandler(BaseHandler):
             origin (str):
             event (synapse.events.EventBase):
             context (synapse.events.snapshot.EventContext):
+
             auth_events (dict[(str, str)->synapse.events.EventBase]):
+                Map from (event_type, state_key) to event
+
+                Normally, our calculated auth_events based on the state of the room
+                at the event's position in the DAG, though occasionally (eg if the
+                event is an outlier), may be the auth events claimed by the remote
+                server.
+
+                Also NB that this function adds entries to it.
 
         Returns:
             defer.Deferred[EventContext]: updated context
         """
         event_auth_events = set(event.auth_event_ids())
 
-        # if the event's auth_events refers to events which are not in our
-        # calculated auth_events, we need to fetch those events from somewhere.
-        #
-        # we start by fetching them from the store, and then try calling /event_auth/.
+        # missing_auth is the set of the event's auth_events which we don't yet have
+        # in auth_events.
         missing_auth = event_auth_events.difference(
             e.event_id for e in auth_events.values()
         )
 
+        # if we have missing events, we need to fetch those events from somewhere.
+        #
+        # we start by checking if they are in the store, and then try calling /event_auth/.
         if missing_auth:
             # TODO: can we use store.have_seen_events here instead?
             have_events = yield self.store.get_seen_events_with_rejections(missing_auth)
-            logger.debug("Got events %s from store", have_events)
+            logger.debug("Found events %s in the store", have_events)
             missing_auth.difference_update(have_events.keys())
         else:
             have_events = {}
@@ -2164,15 +2176,23 @@ class FederationHandler(BaseHandler):
                     event.auth_event_ids()
                 )
             except Exception:
-                # FIXME:
                 logger.exception("Failed to get auth chain")
 
         if event.internal_metadata.is_outlier():
+            # XXX: given that, for an outlier, we'll be working with the
+            # event's *claimed* auth events rather than those we calculated:
+            # (a) is there any point in this test, since different_auth below will
+            # obviously be empty
+            # (b) alternatively, why don't we do it earlier?
             logger.info("Skipping auth_event fetch for outlier")
             return context
 
         # FIXME: Assumes we have and stored all the state for all the
         # prev_events
+        #
+        # FIXME: what does the fixme above mean? where do prev_events come into
+        # it, why do we care about the state for those events, and what does "have and
+        # stored" mean? Seems erik wrote it in c1d860870b
         different_auth = event_auth_events.difference(
             e.event_id for e in auth_events.values()
         )
@@ -2186,6 +2206,9 @@ class FederationHandler(BaseHandler):
             different_auth,
         )
 
+        # now we state-resolve between our own idea of the auth events, and the remote's
+        # idea of them.
+
         room_version = yield self.store.get_room_version(event.room_id)
 
         different_events = yield make_deferred_yieldable(