diff --git a/synapse/storage/events.py b/synapse/storage/events.py
index 6dc46fa50..65b3775f1 100644
--- a/synapse/storage/events.py
+++ b/synapse/storage/events.py
@@ -603,7 +603,6 @@ class EventsStore(SQLBaseStore):
                 "rejections",
                 "redactions",
                 "room_memberships",
-                "state_events",
                 "topics"
             ):
                 txn.executemany(
diff --git a/synapse/storage/schema/delta/35/remove_auth_idx.sql b/synapse/storage/schema/delta/35/remove_auth_idx.sql
deleted file mode 100644
index a5bf3895b..000000000
--- a/synapse/storage/schema/delta/35/remove_auth_idx.sql
+++ /dev/null
@@ -1,16 +0,0 @@
-/* Copyright 2016 OpenMarket Ltd
- *
- * Licensed under the Apache License, Version 2.0 (the "License");
- * you may not use this file except in compliance with the License.
- * You may obtain a copy of the License at
- *
- *    http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
-DROP INDEX IF EXISTS evauth_edges_id;
diff --git a/synapse/storage/schema/delta/36/remove_auth_idx.py b/synapse/storage/schema/delta/36/remove_auth_idx.py
new file mode 100644
index 000000000..deac8ea39
--- /dev/null
+++ b/synapse/storage/schema/delta/36/remove_auth_idx.py
@@ -0,0 +1,83 @@
+# Copyright 2016 OpenMarket Ltd
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from synapse.storage.prepare_database import get_statements
+from synapse.storage.engines import PostgresEngine, Sqlite3Engine
+
+import logging
+
+logger = logging.getLogger(__name__)
+
+DROP_INDICES = """
+-- We only ever query based on event_id
+DROP INDEX IF EXISTS state_events_room_id;
+DROP INDEX IF EXISTS state_events_type;
+DROP INDEX IF EXISTS state_events_state_key;
+
+-- room_id is indexed elsewhere
+DROP INDEX IF EXISTS current_state_events_room_id;
+DROP INDEX IF EXISTS current_state_events_state_key;
+DROP INDEX IF EXISTS current_state_events_type;
+
+DROP INDEX IF EXISTS transactions_have_ref;
+
+-- (topological_ordering, stream_ordering, room_id) seems like a strange index,
+-- and is used incredibly rarely.
+DROP INDEX IF EXISTS events_order_topo_stream_room;
+
+-- TODO: Drop event_auth stuff.
+
+DROP INDEX IF EXISTS event_search_ev_idx;
+"""
+
+POSTGRES_DROP_CONSTRAINT = """
+ALTER TABLE event_auth DROP CONSTRAINT IF EXISTS event_auth_event_id_auth_id_room_id_key;
+"""
+
+SQLITE_DROP_CONSTRAINT = """
+DROP INDEX IF EXISTS evauth_edges_id;
+
+CREATE TABLE IF NOT EXISTS event_auth_new(
+    event_id TEXT NOT NULL,
+    auth_id TEXT NOT NULL,
+    room_id TEXT NOT NULL
+);
+
+INSERT INTO event_auth_new
+    SELECT event_id, auth_id, room_id
+    FROM event_auth;
+
+DROP TABLE event_auth;
+
+ALTER TABLE event_auth_new RENAME TO event_auth;
+
+CREATE INDEX evauth_edges_id ON event_auth(event_id);
+"""
+
+
+def run_create(cur, database_engine, *args, **kwargs):
+    for statement in get_statements(DROP_INDICES.splitlines()):
+        cur.execute(statement)
+
+    if isinstance(database_engine, PostgresEngine):
+        drop_constraint = POSTGRES_DROP_CONSTRAINT
+    else:
+        drop_constraint = SQLITE_DROP_CONSTRAINT
+
+    for statement in get_statements(drop_constraint.splitlines()):
+        cur.execute(statement)
+
+
+def run_upgrade(cur, database_engine, *args, **kwargs):
+    pass