diff --git a/distributed/diagnostics/tests/test_progress.py b/distributed/diagnostics/tests/test_progress.py
index eaab6d0354..5e9ad3269a 100644
--- a/distributed/diagnostics/tests/test_progress.py
+++ b/distributed/diagnostics/tests/test_progress.py
@@ -40,14 +40,17 @@ def h(*args):
 
 
 @nodebug
-@pytest.mark.flaky(reruns=10, reruns_delay=5)
 @gen_cluster(client=True)
 async def test_many_Progress(c, s, a, b):
     x = c.submit(f, 1)
     y = c.submit(g, x)
     z = c.submit(h, y)
 
-    bars = [Progress(keys=[z], scheduler=s) for _ in range(10)]
+    # Give each bar a unique name; otherwise they all tokenize to the same
+    # plugin name and clobber each other in Scheduler.plugins. If z is still
+    # processing when setup() runs (e.g. on slow CI), the second bar's
+    # add_plugin() would then warn "overwriting", which is raised as an error.
+    bars = [Progress(keys=[z], scheduler=s, name=f"progress-{i}") for i in range(10)]
     await asyncio.gather(*(bar.setup() for bar in bars))
     await z