diff --git a/python/ray/data/tests/test_map.py b/python/ray/data/tests/test_map.py
index d690596fd1cf..c06829cfd653 100644
--- a/python/ray/data/tests/test_map.py
+++ b/python/ray/data/tests/test_map.py
@@ -278,34 +278,31 @@ def _get_worker_id(_):
     assert len(unique_worker_ids) == total_blocks
 
 
-def test_concurrency(shutdown_only, target_max_block_size_infinite_or_default):
-    ray.init(num_cpus=6)
-    ds = ray.data.range(10, override_num_blocks=10)
+@pytest.mark.parametrize(
+    "concurrency",
+    [
+        "spam",
+        # Two and three-tuples are valid for callable classes but not for functions.
+        (1, 2),
+        (1, 2, 3),
+        (1, 2, 3, 4),
+    ],
+)
+def test_invalid_func_concurrency_raises(ray_start_regular_shared, concurrency):
+    ds = ray.data.range(1)
+    with pytest.raises(ValueError):
+        ds.map(lambda x: x, concurrency=concurrency)
 
-    def udf(x):
-        return x
 
-    class UDFClass:
-        def __call__(self, x):
-            return x
+@pytest.mark.parametrize("concurrency", ["spam", (1, 2, 3, 4)])
+def test_invalid_class_concurrency_raises(ray_start_regular_shared, concurrency):
+    class Fn:
+        def __call__(self, row):
+            return row
 
-    # Test function and class.
-    for fn in [udf, UDFClass]:
-        # Test concurrency with None, single integer and a tuple of integers.
-        for concurrency in [2, (2, 4), (2, 6, 4)]:
-            if fn == udf and (concurrency == (2, 4) or concurrency == (2, 6, 4)):
-                error_message = "``concurrency`` is set as a tuple of integers"
-                with pytest.raises(ValueError, match=error_message):
-                    ds.map(fn, concurrency=concurrency).take_all()
-            else:
-                result = ds.map(fn, concurrency=concurrency).take_all()
-                assert sorted(extract_values("id", result)) == list(range(10)), result
-
-    # Test concurrency with an illegal value.
-    error_message = "``concurrency`` is expected to be set a"
-    for concurrency in ["dummy", (1, 3, 5, 7)]:
-        with pytest.raises(ValueError, match=error_message):
-            ds.map(UDFClass, concurrency=concurrency).take_all()
+    ds = ray.data.range(1)
+    with pytest.raises(ValueError):
+        ds.map(Fn, concurrency=concurrency)
 
 
 @pytest.mark.parametrize("udf_kind", ["gen", "func"])