diff --git a/synapse/storage/data_stores/main/events_bg_updates.py b/synapse/storage/data_stores/main/events_bg_updates.py
index efee17b92..efb9cd57a 100644
--- a/synapse/storage/data_stores/main/events_bg_updates.py
+++ b/synapse/storage/data_stores/main/events_bg_updates.py
@@ -90,6 +90,22 @@ class EventsBackgroundUpdatesStore(SQLBaseStore):
             "event_store_labels", self._event_store_labels
         )
 
+        self.db.updates.register_background_index_update(
+            "redactions_have_censored_idx",
+            index_name="redactions_have_censored",
+            table="redactions",
+            columns=["event_id"],
+            where_clause="NOT have_censored",
+        )
+
+        self.db.updates.register_background_index_update(
+            "redactions_have_censored_ts_idx",
+            index_name="redactions_have_censored_ts",
+            table="redactions",
+            columns=["received_ts"],
+            where_clause="NOT have_censored",
+        )
+
     @defer.inlineCallbacks
     def _background_reindex_fields_sender(self, progress, batch_size):
         target_min_stream_id = progress["target_min_stream_id_inclusive"]
diff --git a/synapse/storage/data_stores/main/schema/delta/56/redaction_censor.sql b/synapse/storage/data_stores/main/schema/delta/56/redaction_censor.sql
index fe51b0230..a8583b52c 100644
--- a/synapse/storage/data_stores/main/schema/delta/56/redaction_censor.sql
+++ b/synapse/storage/data_stores/main/schema/delta/56/redaction_censor.sql
@@ -14,4 +14,6 @@
  */
 
 ALTER TABLE redactions ADD COLUMN have_censored BOOL NOT NULL DEFAULT false;
-CREATE INDEX redactions_have_censored ON redactions(event_id) WHERE not have_censored;
+
+INSERT INTO background_updates (update_name, progress_json) VALUES
+  ('redactions_have_censored_idx', '{}');
diff --git a/synapse/storage/data_stores/main/schema/delta/56/redaction_censor2.sql b/synapse/storage/data_stores/main/schema/delta/56/redaction_censor2.sql
index 77a5eca49..49ce35d79 100644
--- a/synapse/storage/data_stores/main/schema/delta/56/redaction_censor2.sql
+++ b/synapse/storage/data_stores/main/schema/delta/56/redaction_censor2.sql
@@ -14,7 +14,9 @@
  */
 
 ALTER TABLE redactions ADD COLUMN received_ts BIGINT;
-CREATE INDEX redactions_have_censored_ts ON redactions(received_ts) WHERE not have_censored;
 
 INSERT INTO background_updates (update_name, progress_json) VALUES
   ('redactions_received_ts', '{}');
+
+INSERT INTO background_updates (update_name, progress_json) VALUES
+  ('redactions_have_censored_ts_idx', '{}');