diff --git a/sched/adaptdl_sched/allocator.py b/sched/adaptdl_sched/allocator.py
index 3f30fbf5..4c803693 100644
--- a/sched/adaptdl_sched/allocator.py
+++ b/sched/adaptdl_sched/allocator.py
@@ -59,7 +59,10 @@ async def _allocate_one_loop(self):
                 async for event in watch.stream(
                         self._objs_api.list_namespaced_custom_object,
                         *self._custom_resource, timeout_seconds=60):
-                    if event["type"] == "ADDED":  # there is a n arriving job
+                    # We only consider newly-added preemptible jobs
+                    # because this allocation may not be final.
+                    if (event["type"] == "ADDED" and
+                            event["object"]["spec"]["preemptible"]):
                         async with self._lock:
                             await self._allocate_one(event)