diff --git a/distributed/tests/test_scheduler.py b/distributed/tests/test_scheduler.py
index 1e1a3e69b32..0021d039fed 100644
--- a/distributed/tests/test_scheduler.py
+++ b/distributed/tests/test_scheduler.py
@@ -3218,3 +3218,16 @@ async def test_set_restrictions(c, s, a, b):
     assert s.tasks[f.key].worker_restrictions == {a.address}
     s.reschedule(f)
     await f
+
+
+@gen_cluster(
+    client=True,
+    nthreads=[("", 1, {}), ("", 1, {"memory_pause_fraction": 1e-15}), ("", 1, {})],
+)
+async def test_avoid_paused_workers(c, s, w1, w2, w3):
+    while s.workers[w2.address].status != Status.paused:
+        await asyncio.sleep(0.01)
+    futures = c.map(slowinc, range(8), delay=0.1)
+    w1: Worker
+    while (len(w1.tasks), len(w2.tasks), len(w3.tasks)) != (4, 0, 4):
+        await asyncio.sleep(0.01)