diff --git a/test/t/test_python.py b/test/t/test_python.py
index f9fdfa4b72d..102280d30d0 100644
--- a/test/t/test_python.py
+++ b/test/t/test_python.py
@@ -46,22 +46,41 @@ def test_9(self, completion):
     def test_bb(self, completion):
         assert "-bb" in completion
 
+    @pytest.mark.complete("python foo ", cwd="python")
+    def test_script_args(self, completion):
+        assert "bar.txt" in completion
+
+    @pytest.mark.complete("python -- foo ", cwd="python")
+    def test_script_args_with_double_hyphen(self, completion):
+        assert "bar.txt" in completion
+
     @pytest.mark.complete("python -m foo bar -p ", cwd="python")
-    def test_script_args_1(self, completion):
+    def test_module_args(self, completion):
         assert "bar.txt" in completion
 
-    @pytest.mark.complete("python -mfoo bar -p ", cwd="python")
-    def test_script_args_2(self, completion):
+    @pytest.mark.complete("python foo bar -p ", cwd="python")
+    def test_script_args_after_option(self, completion):
         assert "bar.txt" in completion
 
-    @pytest.mark.complete("python -- foo ", cwd="python")
-    def test_script_args_3(self, completion):
+    @pytest.mark.complete("python -- foo bar -p ", cwd="python")
+    def test_script_args_after_option_with_double_hyphen(self, completion):
+        assert "bar.txt" in completion
+
+    @pytest.mark.complete("python -m foo bar -p ", cwd="python")
+    def test_module_args_after_option(self, completion):
+        assert "bar.txt" in completion
+
+    @pytest.mark.complete("python -mfoo bar -p ", cwd="python")
+    def test_module_args_after_option_with_connected_m_arg(self, completion):
         assert "bar.txt" in completion
 
     @pytest.mark.complete("python -- ", cwd="python")
-    def test_script_args_4(self, completion):
+    def test_script_name(self, completion):
         assert "bar.txt" not in completion
 
     @pytest.mark.complete("python -W -mfoo ", cwd="python")
-    def test_script_args_5(self, completion):
+    def test_fake_module_args_with_w_arg(self, completion):
+        """In this case, -mfoo looks like an option to specify the module, but
+        it should not be treated as the module name because it is an option
+        argument to -W."""
         assert "bar.txt" not in completion