diff --git a/distributed/scheduler.py b/distributed/scheduler.py
index dcb2013c194..ccfc3dbf995 100644
--- a/distributed/scheduler.py
+++ b/distributed/scheduler.py
@@ -2141,11 +2141,24 @@ def decide_worker(self, ts: TaskState) -> WorkerState:
         else:
             worker_pool = self._idle or self._workers
             worker_pool_dv = cast(dict, worker_pool)
+            wp_vals = worker_pool.values()
             n_workers: Py_ssize_t = len(worker_pool_dv)
             if n_workers < 20:  # smart but linear in small case
-                ws = min(worker_pool.values(), key=operator.attrgetter("occupancy"))
+                ws = min(wp_vals, key=operator.attrgetter("occupancy"))
+                if ws._occupancy == 0:
+                    # special case to use round-robin; linear search
+                    # for next worker with zero occupancy (or just
+                    # land back where we started).
+                    wp_i: WorkerState
+                    start: Py_ssize_t = self._n_tasks % n_workers
+                    i: Py_ssize_t
+                    for i in range(n_workers):
+                        wp_i = wp_vals[(i + start) % n_workers]
+                        if wp_i._occupancy == 0:
+                            ws = wp_i
+                            break
             else:  # dumb but fast in large case
-                ws = worker_pool.values()[self._n_tasks % n_workers]
+                ws = wp_vals[self._n_tasks % n_workers]
 
         if self._validate:
             assert ws is None or isinstance(ws, WorkerState), (
diff --git a/distributed/tests/test_client_executor.py b/distributed/tests/test_client_executor.py
index 555bcb86fbe..3942a2ca010 100644
--- a/distributed/tests/test_client_executor.py
+++ b/distributed/tests/test_client_executor.py
@@ -210,26 +210,24 @@ def test_unsupported_arguments(client, s, a, b):
 def test_retries(client):
     args = [ZeroDivisionError("one"), ZeroDivisionError("two"), 42]
 
-    with client.get_executor(retries=3, pure=False) as e:
+    with client.get_executor(retries=5, pure=False) as e:
         future = e.submit(varying(args))
         assert future.result() == 42
 
-    with client.get_executor(retries=2) as e:
+    with client.get_executor(retries=4) as e:
         future = e.submit(varying(args))
         result = future.result()
         assert result == 42
 
-    with client.get_executor(retries=1) as e:
+    with client.get_executor(retries=2) as e:
         future = e.submit(varying(args))
-        with pytest.raises(ZeroDivisionError) as exc_info:
+        with pytest.raises(ZeroDivisionError, match="two"):
             res = future.result()
-        exc_info.match("two")
 
     with client.get_executor(retries=0) as e:
         future = e.submit(varying(args))
-        with pytest.raises(ZeroDivisionError) as exc_info:
+        with pytest.raises(ZeroDivisionError, match="one"):
             res = future.result()
-        exc_info.match("one")
 
 
 def test_shutdown(loop):
diff --git a/distributed/tests/test_scheduler.py b/distributed/tests/test_scheduler.py
index f2fc346d219..c82a4a04839 100644
--- a/distributed/tests/test_scheduler.py
+++ b/distributed/tests/test_scheduler.py
@@ -2234,3 +2234,11 @@ async def test_get_worker_monitor_info(s, a, b):
         assert all(res[w.address]["range_query"][m] is not None for m in ms)
         assert res[w.address]["count"] is not None
         assert res[w.address]["last_time"] is not None
+
+
+@gen_cluster(client=True)
+async def test_quiet_cluster_round_robin(c, s, a, b):
+    await c.submit(inc, 1)
+    await c.submit(inc, 2)
+    await c.submit(inc, 3)
+    assert a.log and b.log