diff --git a/distributed/dashboard/components/scheduler.py b/distributed/dashboard/components/scheduler.py
index d89483472da..cd38f364c8f 100644
--- a/distributed/dashboard/components/scheduler.py
+++ b/distributed/dashboard/components/scheduler.py
@@ -1783,7 +1783,7 @@ def __init__(self, scheduler, **kwargs):
         self.last = 0
         self.source = ColumnDataSource(
             {
-                "time": [time() - 20, time()],
+                "time": [time() - 60, time()],
                 "level": [0, 15],
                 "color": ["white", "white"],
                 "duration": [0, 0],
@@ -1828,7 +1828,7 @@ def convert(self, msgs):
         """Convert a log message to a glyph"""
         total_duration = 0
         for msg in msgs:
-            time, level, key, duration, sat, occ_sat, idl, occ_idl = msg
+            time, level, key, duration, sat, occ_sat, idl, occ_idl = msg[:8]
             total_duration += duration
 
         try:
diff --git a/distributed/stealing.py b/distributed/stealing.py
index 51cfd379a8c..f1539c886e6 100644
--- a/distributed/stealing.py
+++ b/distributed/stealing.py
@@ -237,18 +237,22 @@ def steal_time_ratio(self, ts: TaskState) -> tuple[float, int] | tuple[None, Non
         assert ts.processing_on
         ws = ts.processing_on
         compute_time = ws.processing[ts]
-        if compute_time < 0.005:  # 5ms, just give up
+
+        if not compute_time:
+            # occupancy/ws.proccessing[ts] is only allowed to be zero for
+            # long running tasks which cannot be stolen
+            assert ts in ws.long_running
             return None, None
 
         nbytes = ts.get_nbytes_deps()
         transfer_time = nbytes / self.scheduler.bandwidth + LATENCY
         cost_multiplier = transfer_time / compute_time
-        if cost_multiplier > 100:
-            return None, None
 
         level = int(round(log2(cost_multiplier) + 6))
         if level < 1:
             level = 1
+        elif level >= len(self.cost_multipliers):
+            return None, None
 
         return cost_multiplier, level
 
diff --git a/distributed/tests/test_steal.py b/distributed/tests/test_steal.py
index 6f3874bc1b2..4a3751d6d91 100644
--- a/distributed/tests/test_steal.py
+++ b/distributed/tests/test_steal.py
@@ -10,6 +10,7 @@
 from operator import mul
 from time import sleep
 
+import numpy as np
 import pytest
 from tlz import sliding_window
 
@@ -1350,3 +1351,28 @@ def test_steal_worker_state(ws_with_running_task):
     assert "x" not in ws.tasks
     assert "x" not in ws.data
     assert ws.available_resources == {"R": 1}
+
+
+@pytest.mark.slow()
+@gen_cluster(nthreads=[("", 1)] * 4, client=True)
+async def test_steal_very_fast_tasks(c, s, *workers):
+    # Ensure that very fast tasks are allowed to be stolen
+    root = dask.delayed(lambda n: "x" * n)(
+        dask.utils.parse_bytes("1MiB"), dask_key_name="root"
+    )
+
+    @dask.delayed
+    def func(*args):
+        import time
+
+        time.sleep(0.002)
+
+    ntasks = 1000
+    results = [func(root, i) for i in range(ntasks)]
+    futs = c.compute(results)
+    await c.gather(futs)
+
+    ntasks_per_worker = np.array([len(w.data) for w in workers])
+    ideal = ntasks / len(workers)
+    assert (ntasks_per_worker > ideal * 0.5).all(), (ideal, ntasks_per_worker)
+    assert (ntasks_per_worker < ideal * 1.5).all(), (ideal, ntasks_per_worker)