diff --git a/distributed/tests/test_steal.py b/distributed/tests/test_steal.py
index 4c69b24e7f..f0df021cbd 100644
--- a/distributed/tests/test_steal.py
+++ b/distributed/tests/test_steal.py
@@ -1371,14 +1371,24 @@ def func(*args):
     assert (ntasks_per_worker < ideal * 1.5).all(), (ideal, ntasks_per_worker)
 
 
-def test_balance_steal_communication_heavy_tasks():
-    dependencies = {"a": 10, "b": 10}
+@pytest.mark.parametrize(
+    "cost, ntasks, expect_steal",
+    [
+        pytest.param(10, 5, False, id="not enough work to steal"),
+        pytest.param(10, 10, True, id="enough work to steal"),
+        pytest.param(20, 10, False, id="not enough work for increased cost"),
+    ],
+)
+def test_balance_expensive_tasks(cost, ntasks, expect_steal):
+    dependencies = {"a": cost, "b": cost}
     dependency_placement = [["a"], ["b"]]
-    task_placement = [[["a", "b"]] * 10, []]
+    task_placement = [[["a", "b"]] * ntasks, []]
 
     def _correct_placement(actual):
         actual_task_counts = [len(placed) for placed in actual]
-        return sum(actual_task_counts) == 10 and actual_task_counts[1] > 0
+        return sum(actual_task_counts) == ntasks and (
+            (actual_task_counts[1] > 0) == expect_steal
+        )
 
     _run_dependency_balance_test(
         dependencies,