diff --git a/changelog.d/6615.misc b/changelog.d/6615.misc
new file mode 100644
index 0000000000..9f93152565
--- /dev/null
+++ b/changelog.d/6615.misc
@@ -0,0 +1 @@
+Add some clarifications to `README.md` in the database schema directory.
diff --git a/changelog.d/6954.misc b/changelog.d/6954.misc
new file mode 100644
index 0000000000..8b84ce2f19
--- /dev/null
+++ b/changelog.d/6954.misc
@@ -0,0 +1 @@
+Minor perf fixes to `get_auth_chain_ids`.
diff --git a/synapse/storage/data_stores/main/event_federation.py b/synapse/storage/data_stores/main/event_federation.py
index e16da2577d..750ec1b70d 100644
--- a/synapse/storage/data_stores/main/event_federation.py
+++ b/synapse/storage/data_stores/main/event_federation.py
@@ -16,7 +16,6 @@ import itertools
 import logging
 from typing import List, Optional, Set
 
-from six.moves import range
 from six.moves.queue import Empty, PriorityQueue
 
 from twisted.internet import defer
@@ -28,6 +27,7 @@ from synapse.storage.data_stores.main.events_worker import EventsWorkerStore
 from synapse.storage.data_stores.main.signatures import SignatureWorkerStore
 from synapse.storage.database import Database
 from synapse.util.caches.descriptors import cached
+from synapse.util.iterutils import batch_iter
 
 logger = logging.getLogger(__name__)
 
@@ -88,14 +88,12 @@ class EventFederationWorkerStore(EventsWorkerStore, SignatureWorkerStore, SQLBas
         front = set(event_ids)
         while front:
             new_front = set()
-            front_list = list(front)
-            chunks = [front_list[x : x + 100] for x in range(0, len(front), 100)]
-            for chunk in chunks:
+            for chunk in batch_iter(front, 100):
                 clause, args = make_in_list_sql_clause(
                     txn.database_engine, "event_id", chunk
                 )
-                txn.execute(base_sql + clause, list(args))
-                new_front.update([r[0] for r in txn])
+                txn.execute(base_sql + clause, args)
+                new_front.update(r[0] for r in txn)
 
             new_front -= ignore_events
             new_front -= results
diff --git a/synapse/storage/data_stores/main/schema/full_schemas/README.md b/synapse/storage/data_stores/main/schema/full_schemas/README.md
index bbd3f18604..c00f287190 100644
--- a/synapse/storage/data_stores/main/schema/full_schemas/README.md
+++ b/synapse/storage/data_stores/main/schema/full_schemas/README.md
@@ -1,13 +1,21 @@
-# Building full schema dumps
+# Synapse Database Schemas
 
-These schemas need to be made from a database that has had all background updates run.
+These schemas are used as a basis to create brand new Synapse databases, on both
+SQLite3 and Postgres.
 
-To do so, use `scripts-dev/make_full_schema.sh`. This will produce
-`full.sql.postgres ` and `full.sql.sqlite` files.
+## Building full schema dumps
+
+If you want to recreate these schemas, they need to be made from a database that
+has had all background updates run.
+
+To do so, use `scripts-dev/make_full_schema.sh`. This will produce new
+`full.sql.postgres ` and `full.sql.sqlite` files. 
 
 Ensure postgres is installed and your user has the ability to run bash commands
-such as `createdb`.
+such as `createdb`, then call
 
-```
-./scripts-dev/make_full_schema.sh -p postgres_username -o output_dir/
-```
+    ./scripts-dev/make_full_schema.sh -p postgres_username -o output_dir/
+
+There are currently two folders with full-schema snapshots. `16` is a snapshot
+from 2015, for historical reference. The other contains the most recent full
+schema snapshot.
diff --git a/synapse/storage/database.py b/synapse/storage/database.py
index 3eeb2f7c04..6dcb5c04da 100644
--- a/synapse/storage/database.py
+++ b/synapse/storage/database.py
@@ -1504,7 +1504,7 @@ class Database(object):
 
 def make_in_list_sql_clause(
     database_engine, column: str, iterable: Iterable
-) -> Tuple[str, Iterable]:
+) -> Tuple[str, list]:
     """Returns an SQL clause that checks the given column is in the iterable.
 
     On SQLite this expands to `column IN (?, ?, ...)`, whereas on Postgres