diff --git a/distributed/scheduler.py b/distributed/scheduler.py
index 9c25d2c85b..3217436d09 100644
--- a/distributed/scheduler.py
+++ b/distributed/scheduler.py
@@ -18,7 +18,7 @@
 from datetime import timedelta
 from functools import partial
 from numbers import Number
-from typing import Optional
+from typing import Optional, ValuesView
 
 import psutil
 import sortedcontainers
@@ -2387,7 +2387,10 @@ def decide_worker(self, ts: TaskState) -> WorkerState:
         if ts._dependencies or valid_workers is not None:
             ws = decide_worker(
                 ts,
-                self._workers_dv.values(),
+                dict.values(self._workers_dv),
+                dict.values(self._idle_dv),
+                # ^ NOTE: For performance, these must be actual `dict_values`, not `SortedDictValues`.
+                # In Cython, `_workers_dv` is a plain dict, but in plain Python, it's still a `SortedDict`.
                 valid_workers,
                 partial(self.worker_objective, ts),
             )
@@ -7623,14 +7626,19 @@ def _reevaluate_occupancy_worker(state: SchedulerState, ws: WorkerState):
 @cfunc
 @exceptval(check=False)
 def decide_worker(
-    ts: TaskState, all_workers, valid_workers: set, objective
+    ts: TaskState,
+    all_workers: ValuesView,
+    idle_workers: ValuesView,
+    valid_workers: set,
+    objective,
 ) -> WorkerState:
     """
     Decide which worker should take task *ts*.
 
-    We choose the worker that has the data on which *ts* depends.
+    We consider all workers which hold dependencies of *ts*,
+    plus a sample of up to 10 random workers (with preference for idle ones).
 
-    If several workers have dependencies then we choose the less-busy worker.
+    From those, we choose the worker where the *objective* function is minimized.
 
     Optionally provide *valid_workers* of where jobs are allowed to occur
     (if all workers are allowed to take the task, pass None instead).
@@ -7640,6 +7648,8 @@ def decide_worker(
     of bytes sent between workers.  This is determined by calling the
     *objective* function.
     """
+    # NOTE: `all_workers` and `idle_workers` must be plain `dict_values` objects,
+    # not a `SortedValuesView`, which is much slower to iterate over.
     ws: WorkerState = None
     wws: WorkerState
     dts: TaskState
@@ -7649,7 +7659,17 @@ def decide_worker(
     if ts._actor:
         candidates = set(all_workers)
     else:
+        # Select all workers holding deps of this task
         candidates = {wws for dts in deps for wws in dts._who_has}
+        # Add up to 10 random workers into `candidates`, preferring idle ones.
+        worker_pool = valid_workers if valid_workers is not None else all_workers
+        if len(candidates) < len(worker_pool):
+            sample_from = idle_workers or worker_pool
+            candidates.update(
+                random.choices(list(sample_from), k=min(10, len(sample_from)))
+                if len(sample_from) > 10
+                else sample_from
+            )
     if valid_workers is None:
         if not candidates:
             candidates = set(all_workers)
@@ -7659,7 +7679,7 @@ def decide_worker(
             candidates = valid_workers
             if not candidates:
                 if ts._loose_restrictions:
-                    ws = decide_worker(ts, all_workers, None, objective)
+                    ws = decide_worker(ts, all_workers, idle_workers, None, objective)
                 return ws
 
     ncandidates: Py_ssize_t = len(candidates)
diff --git a/distributed/tests/test_scheduler.py b/distributed/tests/test_scheduler.py
index 6a15109178..340965019f 100644
--- a/distributed/tests/test_scheduler.py
+++ b/distributed/tests/test_scheduler.py
@@ -101,14 +101,16 @@ async def test_recompute_released_results(c, s, a, b):
     assert result == 1
 
 
-@gen_cluster(client=True)
+@gen_cluster(client=True, config={"distributed.scheduler.bandwidth": "1Mb"})
 async def test_decide_worker_with_many_independent_leaves(c, s, a, b):
+    # Make data large to penalize scheduling dependent tasks on other workers
+    ballast = b"\0" * int(s.bandwidth)
     xs = await asyncio.gather(
-        c.scatter(list(range(0, 100, 2)), workers=a.address),
-        c.scatter(list(range(1, 100, 2)), workers=b.address),
+        c.scatter([bytes(i) + ballast for i in range(0, 100, 2)], workers=a.address),
+        c.scatter([bytes(i) + ballast for i in range(1, 100, 2)], workers=b.address),
     )
     xs = list(concat(zip(*xs)))
-    ys = [delayed(inc)(x) for x in xs]
+    ys = [delayed(lambda s: s[0])(x) for x in xs]
 
     y2s = c.persist(ys)
     await wait(y2s)
@@ -127,6 +129,27 @@ async def test_decide_worker_with_restrictions(client, s, a, b, c):
     assert x.key in a.data or x.key in b.data
 
 
+@gen_cluster(
+    client=True,
+    nthreads=[("127.0.0.1", 1)] * 3,
+    config={"distributed.scheduler.work-stealing": False},
+)
+async def test_decide_worker_select_candidate_holding_no_deps(client, s, a, b, c):
+    await client.submit(slowinc, 10, delay=0.1)  # learn that slowinc is slow
+    root = await client.scatter(1)
+    assert sum(root.key in worker.data for worker in [a, b, c]) == 1
+
+    start = time()
+    tasks = client.map(slowinc, [root] * 6, delay=0.1, pure=False)
+    await wait(tasks)
+    elapsed = time() - start
+
+    assert elapsed <= 4
+    assert all(root.key in worker.data for worker in [a, b, c]), [
+        list(worker.data.keys()) for worker in [a, b, c]
+    ]
+
+
 @pytest.mark.parametrize("ndeps", [0, 1, 4])
 @pytest.mark.parametrize(
     "nthreads",
diff --git a/distributed/tests/test_worker.py b/distributed/tests/test_worker.py
index e5e877a2a9..4c0c3886ce 100644
--- a/distributed/tests/test_worker.py
+++ b/distributed/tests/test_worker.py
@@ -1079,8 +1079,8 @@ async def test_scheduler_delay(c, s, a, b):
 
 
 @pytest.mark.flaky(reruns=10, reruns_delay=5)
-@gen_cluster(client=True)
-async def test_statistical_profiling(c, s, a, b):
+@gen_cluster(client=True, ncores=[("127.0.0.1", 1)])
+async def test_statistical_profiling(c, s, a):
     futures = c.map(slowinc, range(10), delay=0.1)
     await wait(futures)