diff --git a/distributed/tests/test_speculative.py b/distributed/tests/test_speculative.py
index e1177bbb134..9d12f817c2f 100644
--- a/distributed/tests/test_speculative.py
+++ b/distributed/tests/test_speculative.py
@@ -1,19 +1,27 @@
+import asyncio
+
 from dask import delayed
 
-from distributed.utils_test import gen_cluster, inc, dec
+from distributed.utils_test import gen_cluster, inc, dec, slowinc
 
 
 @gen_cluster(client=True, config={"dask.optimization.fuse.active": False})
 async def test_speculative_assignment_simple(c, s, a, b):
-    x = delayed(inc)(1)
+    x = delayed(slowinc)(1)
     y = delayed(inc)(x)
     z = delayed(dec)(y)
 
-    zz = c.compute(z)
-    result = await zz
-    assert result == 2
-    assert (y.key, "speculative", "ready") in a.story(y.key)
-    assert (z.key, "speculative", "ready") in a.story(z.key)
+    result = c.compute(z)
+    while not a.tasks:
+        await asyncio.sleep(0.001)
+
+    assert y.key in a.tasks
+    assert z.key in a.tasks
+
+    assert a.tasks[y.key].state == "speculative"
+    assert a.tasks[z.key].state == "speculative"
+
+    assert await result == 2
 
 
 @gen_cluster(client=True, config={"dask.optimization.fuse.active": False})
@@ -48,7 +56,7 @@ async def test_spec_assign_intermittent(c, s, a, b):
       f   i   # both spec
       |   |
       g   j   # both spec
-       \ /
+       \ /                                 # noqa
         k     # spec
 
     """