diff --git a/test/test_pseudo_python_cli.py b/test/test_pseudo_python_cli.py
index 2a4d5562..7a90cda9 100644
--- a/test/test_pseudo_python_cli.py
+++ b/test/test_pseudo_python_cli.py
@@ -20,13 +20,35 @@ def make_dict(**kwargs):
     ("-m ipykernel_launcher -f FILE",
      make_dict(module="ipykernel_launcher",
                args=shlex.split("-f FILE"))),
+    ("-", make_dict(script="-")),
+    ("- a", make_dict(script="-", args=["a"])),
+    ("script", make_dict(script="script")),
+    ("script a", make_dict(script="script", args=["a"])),
 ])
-def test_parse_args(args, desired):
+def test_valid_args(args, desired):
     ns = parse_args(shlex.split(args))
     actual = vars(ns)
     assert actual == desired
 
 
+@pytest.mark.parametrize("args", [
+    "-m",
+    "-c",
+    "-i -m",
+    # They are invalid in python CLI but works in argparse (which is
+    # probably OK):
+    pytest.mark.xfail("-V -m"),
+    pytest.mark.xfail("-h -m"),
+])
+def test_invalid_args(args, capsys):
+    with pytest.raises(SystemExit) as exc_info:
+        parse_args(shlex.split(args))
+    assert exc_info.value.code != 0
+
+    captured = capsys.readouterr()
+    assert "usage:" in captured.err
+
+
 @pytest.mark.parametrize("cli_args", [
     ["-h"],
     ["-i", "--help"],