diff --git a/synapse/storage/util/id_generators.py b/synapse/storage/util/id_generators.py
index 0d7108f01b41..b4d527808d21 100644
--- a/synapse/storage/util/id_generators.py
+++ b/synapse/storage/util/id_generators.py
@@ -699,20 +699,23 @@ def _add_persisted_position(self, new_id: int) -> None:
         # current position to the latest position seen. This allows the instance
         # to report a recent position when asked, rather than a potentially old
         # one (if this instance hasn't written anything for a while).
-        our_current_position = self._current_positions.get(self._instance_name)
-        if (
-            our_current_position
-            and not self._unfinished_ids
-            and not self._in_flight_fetches
-        ):
-            self._current_positions[self._instance_name] = max(
-                our_current_position, new_id
-            )
 
         # We move the current min position up if the minimum current positions
         # of all instances is higher (since by definition all positions less
         # that that have been persisted).
-        min_curr = min(self._current_positions.values(), default=0)
+        min_curr = min(
+            (
+                token
+                for name, token in self._current_positions.items()
+                if name != self._instance_name
+            ),
+            default=0,
+        )
+
+        our_current_position = self._current_positions.get(self._instance_name)
+        if our_current_position and (self._unfinished_ids or self._in_flight_fetches):
+            min_curr = min(min_curr, our_current_position)
+
         self._persisted_upto_position = max(min_curr, self._persisted_upto_position)
 
         # We now iterate through the seen positions, discarding those that are