diff --git a/tests/test_cache_executor_serial.py b/tests/test_cache_executor_serial.py
index f0cffe9d..6cb2465e 100644
--- a/tests/test_cache_executor_serial.py
+++ b/tests/test_cache_executor_serial.py
@@ -167,6 +167,12 @@ def test_executor_function_dependence_args(self):
         q.put({"shutdown": True, "wait": True})
         process.join()
 
+    def test_execute_in_subprocess_errors(self):
+        with self.assertRaises(ValueError):
+            execute_in_subprocess(command=[], config_directory="test")
+        with self.assertRaises(ValueError):
+            execute_in_subprocess(command=[], backend="flux")
+
     def tearDown(self):
         if os.path.exists("cache"):
             shutil.rmtree("cache")
diff --git a/tests/test_cache_hdf.py b/tests/test_cache_hdf.py
index f7143f3e..a13a4d9d 100644
--- a/tests/test_cache_hdf.py
+++ b/tests/test_cache_hdf.py
@@ -4,7 +4,7 @@
 
 
 try:
-    from executorlib.standalone.hdf import dump, load
+    from executorlib.standalone.hdf import dump, load, get_output
 
     skip_h5py_test = False
 except ImportError:
@@ -33,6 +33,9 @@ def test_hdf_mixed(self):
         self.assertTrue("fn" in data_dict.keys())
         self.assertEqual(data_dict["args"], [a])
         self.assertEqual(data_dict["kwargs"], {"b": b})
+        flag, output = get_output(file_name=file_name)
+        self.assertFalse(flag)
+        self.assertIsNone(output)
 
     def test_hdf_args(self):
         cache_directory = os.path.abspath("cache")
@@ -45,6 +48,9 @@ def test_hdf_args(self):
         self.assertTrue("fn" in data_dict.keys())
         self.assertEqual(data_dict["args"], [a, b])
         self.assertEqual(data_dict["kwargs"], {})
+        flag, output = get_output(file_name=file_name)
+        self.assertFalse(flag)
+        self.assertIsNone(output)
 
     def test_hdf_kwargs(self):
         cache_directory = os.path.abspath("cache")
@@ -60,6 +66,9 @@ def test_hdf_kwargs(self):
         self.assertTrue("fn" in data_dict.keys())
         self.assertEqual(data_dict["args"], ())
         self.assertEqual(data_dict["kwargs"], {"a": a, "b": b})
+        flag, output = get_output(file_name=file_name)
+        self.assertFalse(flag)
+        self.assertIsNone(output)
 
     def tearDown(self):
         if os.path.exists("cache"):
diff --git a/tests/test_executor_backend_mpi_noblock.py b/tests/test_executor_backend_mpi_noblock.py
index 06be8a4d..1440d5e9 100644
--- a/tests/test_executor_backend_mpi_noblock.py
+++ b/tests/test_executor_backend_mpi_noblock.py
@@ -13,11 +13,27 @@ def resource_dict(resource_dict):
 
 
 class TestExecutorBackend(unittest.TestCase):
-    def test_meta_executor_serial(self):
+    def test_meta_executor_serial_with_dependencies(self):
         with Executor(
             max_cores=2,
             backend="local",
             block_allocation=False,
+            disable_dependencies=True,
+        ) as exe:
+            cloudpickle_register(ind=1)
+            fs_1 = exe.submit(calc, 1)
+            fs_2 = exe.submit(calc, 2)
+            self.assertEqual(fs_1.result(), 1)
+            self.assertEqual(fs_2.result(), 2)
+            self.assertTrue(fs_1.done())
+            self.assertTrue(fs_2.done())
+
+    def test_meta_executor_serial_without_dependencies(self):
+        with Executor(
+            max_cores=2,
+            backend="local",
+            block_allocation=False,
+            disable_dependencies=False,
         ) as exe:
             cloudpickle_register(ind=1)
             fs_1 = exe.submit(calc, 1)