diff --git a/changelog.d/7567.misc b/changelog.d/7567.misc
new file mode 100644
index 000000000..b086d5d02
--- /dev/null
+++ b/changelog.d/7567.misc
@@ -0,0 +1 @@
+Improve query performance for fetching state from a PostgreSQL database.
diff --git a/synapse/storage/data_stores/state/bg_updates.py b/synapse/storage/data_stores/state/bg_updates.py
index e8edaf9f7..ff000bc9e 100644
--- a/synapse/storage/data_stores/state/bg_updates.py
+++ b/synapse/storage/data_stores/state/bg_updates.py
@@ -109,20 +109,20 @@ class StateGroupBackgroundUpdateStore(SQLBaseStore):
                     SELECT prev_state_group FROM state_group_edges e, state s
                     WHERE s.state_group = e.state_group
                 )
-                SELECT DISTINCT type, state_key, last_value(event_id) OVER (
-                    PARTITION BY type, state_key ORDER BY state_group ASC
-                    ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING
-                ) AS event_id FROM state_groups_state
+                SELECT DISTINCT ON (type, state_key)
+                    type, state_key, event_id
+                FROM state_groups_state
                 WHERE state_group IN (
                     SELECT state_group FROM state
-                )
+                ) %s
+                ORDER BY type, state_key, state_group DESC
             """
 
             for group in groups:
                 args = [group]
                 args.extend(where_args)
 
-                txn.execute(sql + where_clause, args)
+                txn.execute(sql % (where_clause,), args)
                 for row in txn:
                     typ, state_key, event_id = row
                     key = (typ, state_key)