diff --git a/alembic/versions/9813b7160e69_parametrize_test_large_map.py b/alembic/versions/9813b7160e69_parametrize_test_large_map.py
new file mode 100644
index 0000000000..3f7519a407
--- /dev/null
+++ b/alembic/versions/9813b7160e69_parametrize_test_large_map.py
@@ -0,0 +1,30 @@
+"""Parametrize test_large_map
+
+Revision ID: 9813b7160e69
+Revises: f459b2c61eaf
+Create Date: 2023-07-05 11:04:08.510205
+
+"""
+from alembic import op
+
+
+# revision identifiers, used by Alembic.
+revision = '9813b7160e69'
+down_revision = 'f459b2c61eaf'
+branch_labels = None
+depends_on = None
+
+
+def upgrade() -> None:
+    op.execute(
+        """
+        update test_run 
+        set name = 'test_large_map[rootish]' 
+        where name == 'test_large_map';
+        """
+    )
+
+def downgrade() -> None:
+    # ### commands auto generated by Alembic - please adjust! ###
+    pass
+    # ### end Alembic commands ###
diff --git a/tests/benchmarks/test_futures.py b/tests/benchmarks/test_futures.py
index be46575c29..ffc490836e 100644
--- a/tests/benchmarks/test_futures.py
+++ b/tests/benchmarks/test_futures.py
@@ -17,9 +17,19 @@ def test_single_future(small_client):
 
 
 @run_up_to_nthreads("small_cluster", 50, reason="fixed dataset")
-def test_large_map(small_client):
+@pytest.mark.parametrize("rootish", ["rootish", "non-rootish"])
+def test_large_map(small_client, rootish):
     """What's the overhead of map these days?"""
-    futures = small_client.map(inc, range(100_000))
+    if rootish == "rootish":
+        futures = small_client.map(inc, range(100_000))
+    else:
+
+        def inc_with_deps(i, deps):
+            return i + 1
+
+        deps = small_client.map(inc, range(5))
+        futures = small_client.map(inc_with_deps, range(100_000), deps=deps)
+
     wait(futures)