diff --git a/src/test/test-argv-util.c b/src/test/test-argv-util.c
index 5bf2903658..f7b8f9478b 100644
--- a/src/test/test-argv-util.c
+++ b/src/test/test-argv-util.c
@@ -122,6 +122,11 @@ TEST(argv_help) {
         assert_se(argv_looks_like_help(4, STRV_MAKE("program", "arg1", "arg2", "-h")));
         assert_se(!argv_looks_like_help(2, STRV_MAKE("program", "arg1")));
         assert_se(!argv_looks_like_help(4, STRV_MAKE("program", "arg1", "arg2", "--h")));
+        assert_se(!argv_looks_like_help(3, STRV_MAKE("program", "Help", "arg2")));
+        assert_se(argv_looks_like_help(5, STRV_MAKE("program", "--help", "arg1", "-h", "--help")));
+        assert_se(!argv_looks_like_help(4, STRV_MAKE("program","arg1", "arg2", "-H")));
+        assert_se(!argv_looks_like_help(3, STRV_MAKE("program", "--Help", "arg2")));
+
 }
 
 static int intro(void) {