diff --git a/synapse/storage/background_updates.py b/synapse/storage/background_updates.py
index f473294070..efe4238036 100644
--- a/synapse/storage/background_updates.py
+++ b/synapse/storage/background_updates.py
@@ -44,7 +44,7 @@ from synapse._pydantic_compat import HAS_PYDANTIC_V2
 from synapse.metrics.background_process_metrics import run_as_background_process
 from synapse.storage.engines import PostgresEngine
 from synapse.storage.types import Connection, Cursor
-from synapse.types import JsonDict
+from synapse.types import JsonDict, StrCollection
 from synapse.util import Clock, json_encoder
 
 from . import engines
@@ -487,6 +487,25 @@ class BackgroundUpdater:
 
         return not update_exists
 
+    async def have_completed_background_updates(
+        self, update_names: StrCollection
+    ) -> bool:
+        """Return the name of background updates that have not yet been
+        completed"""
+        if self._all_done:
+            return True
+
+        rows = await self.db_pool.simple_select_many_batch(
+            table="background_updates",
+            column="update_name",
+            iterable=update_names,
+            retcols=("update_name",),
+            desc="get_uncompleted_background_updates",
+        )
+
+        # If we find any rows then we've not completed the update.
+        return not bool(rows)
+
     async def do_next_background_update(self, sleep: bool = True) -> bool:
         """Does some amount of work on the next queued background update
 
diff --git a/synapse/storage/databases/main/events_bg_updates.py b/synapse/storage/databases/main/events_bg_updates.py
index e97b177dd6..c6c8eeaa02 100644
--- a/synapse/storage/databases/main/events_bg_updates.py
+++ b/synapse/storage/databases/main/events_bg_updates.py
@@ -2275,16 +2275,11 @@ class EventsBackgroundUpdatesStore(StreamWorkerStore, StateDeltasStore, SQLBaseS
     async def have_finished_sliding_sync_background_jobs(self) -> bool:
         """Return if its safe to use the sliding sync membership tables."""
 
-        # TODO: Find a more efficient way of checking this. A cache?
-        return (
-            await self.db_pool.updates.has_completed_background_update(
-                _BackgroundUpdates.SLIDING_SYNC_PREFILL_JOINED_ROOMS_TO_RECALCULATE_TABLE_BG_UPDATE
-            )
-            or await self.db_pool.updates.has_completed_background_update(
-                _BackgroundUpdates.SLIDING_SYNC_JOINED_ROOMS_BG_UPDATE
-            )
-            or await self.db_pool.updates.has_completed_background_update(
-                _BackgroundUpdates.SLIDING_SYNC_MEMBERSHIP_SNAPSHOTS_BG_UPDATE
+        return await self.db_pool.updates.have_completed_background_updates(
+            (
+                _BackgroundUpdates.SLIDING_SYNC_PREFILL_JOINED_ROOMS_TO_RECALCULATE_TABLE_BG_UPDATE,
+                _BackgroundUpdates.SLIDING_SYNC_JOINED_ROOMS_BG_UPDATE,
+                _BackgroundUpdates.SLIDING_SYNC_MEMBERSHIP_SNAPSHOTS_BG_UPDATE,
             )
         )