diff --git a/changelog.d/15068.bugfix b/changelog.d/15068.bugfix
new file mode 100644
index 000000000..f09ffa287
--- /dev/null
+++ b/changelog.d/15068.bugfix
@@ -0,0 +1 @@
+Fix a bug introduced in Synapse 1.76.0 where partially-joined rooms could not be deleted using the [purge room API](https://matrix-org.github.io/synapse/latest/admin_api/rooms.html#delete-room-api).
diff --git a/synapse/handlers/federation.py b/synapse/handlers/federation.py
index 08727e485..1d0f6bcd6 100644
--- a/synapse/handlers/federation.py
+++ b/synapse/handlers/federation.py
@@ -1880,6 +1880,11 @@ class FederationHandler:
                 logger.info("Updating current state for %s", room_id)
                 # TODO(faster_joins): notify workers in notify_room_un_partial_stated
                 #   https://github.com/matrix-org/synapse/issues/12994
+                #
+                # NB: there's a potential race here. If room is purged just before we
+                # call this, we _might_ end up inserting rows into current_state_events.
+                # (The logic is hard to chase through.) We think this is fine, but if
+                # not the HS admin should purge the room again.
                 await self.state_handler.update_current_state(room_id)
 
                 logger.info("Handling any pending device list updates")
diff --git a/synapse/storage/databases/main/purge_events.py b/synapse/storage/databases/main/purge_events.py
index 9213ce0b5..9c41d01e1 100644
--- a/synapse/storage/databases/main/purge_events.py
+++ b/synapse/storage/databases/main/purge_events.py
@@ -420,12 +420,14 @@ class PurgeEventsStore(StateGroupWorkerStore, CacheInvalidationWorkerStore):
             "event_push_actions",
             "event_search",
             "event_failed_pull_attempts",
+            # Note: the partial state tables have foreign keys between each other, and to
+            # `events` and `rooms`. We need to delete from them in the right order.
             "partial_state_events",
+            "partial_state_rooms_servers",
+            "partial_state_rooms",
             "events",
             "federation_inbound_events_staging",
             "local_current_membership",
-            "partial_state_rooms_servers",
-            "partial_state_rooms",
             "receipts_graph",
             "receipts_linearized",
             "room_aliases",