diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 00bf152..de84f2e 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -42,7 +42,7 @@ run optional_test_inplace_factory.cpp ;
 run optional_test_io.cpp ;
 run optional_test_move.cpp ;
 run optional_test_noexcept_move.cpp ;
-run optional_test_equals_none.cpp ;
+run optional_test_cmp_none.cpp ;
 run optional_test_value_access.cpp ;
 run optional_test_emplace.cpp ;
 run optional_test_minimum_requirements.cpp ;
diff --git a/test/optional_test_cmp_none.cpp b/test/optional_test_cmp_none.cpp
new file mode 100644
index 0000000..691517b
--- /dev/null
+++ b/test/optional_test_cmp_none.cpp
@@ -0,0 +1,83 @@
+// Copyright (C) 2014 Andrzej Krzemienski.
+// Copyright (C) 2024 Alexander Grund
+//
+// Use, modification, and distribution is subject to the Boost Software
+// License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+//
+// See http://www.boost.org/lib/optional for documentation.
+//
+// You are welcome to contact the author at:
+//  akrzemi1@gmail.com
+
+#include "boost/optional/optional.hpp"
+
+#ifdef BOOST_BORLANDC
+#pragma hdrstop
+#endif
+
+#include "boost/core/lightweight_test.hpp"
+#include "boost/none.hpp"
+
+
+struct SemiRegular // no operator==
+{ 
+private: void operator==(SemiRegular const&) const {}
+private: void operator!=(SemiRegular const&) const {}
+};
+
+void test_equal_to_none_of_noncomparable_T()
+{
+  boost::optional<SemiRegular> i = SemiRegular();
+  boost::optional<SemiRegular> o;
+  
+  BOOST_TEST(i != boost::none);
+  BOOST_TEST(boost::none != i);
+  BOOST_TEST(o == boost::none);
+  BOOST_TEST(boost::none == o);
+}
+
+void test_comparison_to_none()
+{
+    using boost::none;
+    boost::optional<SemiRegular> i = SemiRegular();
+    // the default ordering of optional<size_t> is{ boost::none, 0, 1, 2, ... }
+    // Hence boost::none < i for any engaged i
+    // and all others operators ( ==, !=, <, <=, >, >= ) follow
+
+    BOOST_TEST(!(i == none));
+    BOOST_TEST(i != none);
+    BOOST_TEST(!(i < none));
+    BOOST_TEST(!(i <= none));
+    BOOST_TEST(i > none);
+    BOOST_TEST(i >= none);
+    // Comparison is symmetric
+    BOOST_TEST(!(none == i));
+    BOOST_TEST(none != i);
+    BOOST_TEST(none < i);
+    BOOST_TEST(none <= i);
+    BOOST_TEST(!(none > i));
+    BOOST_TEST(!(none >= i));
+
+    // An un-engaged optional is always equal to none
+    boost::optional<SemiRegular> o;
+    BOOST_TEST(o == none);
+    BOOST_TEST(!(o != none));
+    BOOST_TEST(!(o < none));
+    BOOST_TEST(o <= none);
+    BOOST_TEST(!(o > none));
+    BOOST_TEST(o >= none);
+    // Comparison is symmetric
+    BOOST_TEST(none == o);
+    BOOST_TEST(!(none != o));
+    BOOST_TEST(!(none < o));
+    BOOST_TEST(none <= o);
+    BOOST_TEST(!(none > o));
+    BOOST_TEST(none >= o);
+}
+
+int main()
+{
+  test_equal_to_none_of_noncomparable_T();
+  return boost::report_errors();
+}
diff --git a/test/optional_test_equals_none.cpp b/test/optional_test_equals_none.cpp
deleted file mode 100644
index 1e3157b..0000000
--- a/test/optional_test_equals_none.cpp
+++ /dev/null
@@ -1,43 +0,0 @@
-// Copyright (C) 2014 Andrzej Krzemienski.
-//
-// Use, modification, and distribution is subject to the Boost Software
-// License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
-// http://www.boost.org/LICENSE_1_0.txt)
-//
-// See http://www.boost.org/lib/optional for documentation.
-//
-// You are welcome to contact the author at:
-//  akrzemi1@gmail.com
-
-#include "boost/optional/optional.hpp"
-
-#ifdef BOOST_BORLANDC
-#pragma hdrstop
-#endif
-
-#include "boost/core/lightweight_test.hpp"
-#include "boost/none.hpp"
-
-
-struct SemiRegular // no operator==
-{ 
-private: void operator==(SemiRegular const&) const {}
-private: void operator!=(SemiRegular const&) const {}
-};
-
-void test_equal_to_none_of_noncomparable_T()
-{
-  boost::optional<SemiRegular> i = SemiRegular();
-  boost::optional<SemiRegular> o;
-  
-  BOOST_TEST(i != boost::none);
-  BOOST_TEST(boost::none != i);
-  BOOST_TEST(o == boost::none);
-  BOOST_TEST(boost::none == o);
-}
-
-int main()
-{
-  test_equal_to_none_of_noncomparable_T();
-  return boost::report_errors();
-}