diff --git a/libstdc++-v3/libsupc++/compare b/libstdc++-v3/libsupc++/compare
index 82d00889272..b1f342113f1 100644
--- a/libstdc++-v3/libsupc++/compare
+++ b/libstdc++-v3/libsupc++/compare
@@ -600,6 +600,9 @@ namespace std
 	  // FIXME: || floating_point<remove_reference_t<_Tp>>
 	  || __cmp3way<strong_ordering, _Tp, _Up>;
 
+    template<typename _Tp, typename _Up>
+      concept __decayed_same_as = same_as<decay_t<_Tp>, decay_t<_Up>>;
+
     class _Strong_order
     {
       template<typename _Tp, typename _Up>
@@ -620,14 +623,12 @@ namespace std
       friend class _Strong_fallback;
 
     public:
-      template<typename _Tp, typename _Up>
+      template<typename _Tp, __decayed_same_as<_Tp> _Up>
 	requires __strongly_ordered<_Tp, _Up>
 	constexpr strong_ordering
 	operator()(_Tp&& __e, _Up&& __f) const
 	noexcept(_S_noexcept<_Tp, _Up>())
 	{
-	  static_assert(same_as<decay_t<_Tp>, decay_t<_Up>>);
-
 	  /* FIXME:
 	  if constexpr (floating_point<decay_t<_Tp>>)
 	    return __cmp_cust::__fp_strong_order(__e, __f);
@@ -669,14 +670,12 @@ namespace std
       friend class _Weak_fallback;
 
     public:
-      template<typename _Tp, typename _Up>
+      template<typename _Tp, __decayed_same_as<_Tp> _Up>
 	requires __weakly_ordered<_Tp, _Up>
 	constexpr weak_ordering
 	operator()(_Tp&& __e, _Up&& __f) const
 	noexcept(_S_noexcept<_Tp, _Up>())
 	{
-	  static_assert(same_as<decay_t<_Tp>, decay_t<_Up>>);
-
 	  if constexpr (floating_point<decay_t<_Tp>>)
 	    return __cmp_cust::__fp_weak_ordering(__e, __f);
 	  else if constexpr (__adl_weak<_Tp, _Up>)
@@ -716,14 +715,12 @@ namespace std
       friend class _Partial_fallback;
 
     public:
-      template<typename _Tp, typename _Up>
+      template<typename _Tp, __decayed_same_as<_Tp> _Up>
 	requires __partially_ordered<_Tp, _Up>
 	constexpr partial_ordering
 	operator()(_Tp&& __e, _Up&& __f) const
 	noexcept(_S_noexcept<_Tp, _Up>())
 	{
-	  static_assert(same_as<decay_t<_Tp>, decay_t<_Up>>);
-
 	  if constexpr (__adl_partial<_Tp, _Up>)
 	    return partial_ordering(partial_order(static_cast<_Tp&&>(__e),
 						  static_cast<_Up&&>(__f)));
@@ -759,18 +756,16 @@ namespace std
 	}
 
     public:
-      template<typename _Tp, typename _Up>
+      template<typename _Tp, __decayed_same_as<_Tp> _Up>
 	requires __strongly_ordered<_Tp, _Up> || __op_eq_lt<_Tp, _Up>
-	constexpr decltype(auto)
+	constexpr strong_ordering
 	operator()(_Tp&& __e, _Up&& __f) const
 	noexcept(_S_noexcept<_Tp, _Up>())
 	{
-	  static_assert(same_as<decay_t<_Tp>, decay_t<_Up>>);
-
 	  if constexpr (__strongly_ordered<_Tp, _Up>)
 	    return _Strong_order{}(static_cast<_Tp&&>(__e),
 				   static_cast<_Up&&>(__f));
-	  else if constexpr (__op_eq_lt<_Tp, _Up>)
+	  else // __op_eq_lt<_Tp, _Up>
 	    return static_cast<_Tp&&>(__e) == static_cast<_Up&&>(__f)
 	      ? strong_ordering::equal
 	      : static_cast<_Tp&&>(__e) < static_cast<_Up&&>(__f)
@@ -793,18 +788,16 @@ namespace std
 	}
 
     public:
-      template<typename _Tp, typename _Up>
+      template<typename _Tp, __decayed_same_as<_Tp> _Up>
 	requires __weakly_ordered<_Tp, _Up> || __op_eq_lt<_Tp, _Up>
-	constexpr decltype(auto)
+	constexpr weak_ordering
 	operator()(_Tp&& __e, _Up&& __f) const
 	noexcept(_S_noexcept<_Tp, _Up>())
 	{
-	  static_assert(same_as<decay_t<_Tp>, decay_t<_Up>>);
-
 	  if constexpr (__weakly_ordered<_Tp, _Up>)
 	    return _Weak_order{}(static_cast<_Tp&&>(__e),
 				 static_cast<_Up&&>(__f));
-	  else if constexpr (__op_eq_lt<_Tp, _Up>)
+	  else // __op_eq_lt<_Tp, _Up>
 	    return static_cast<_Tp&&>(__e) == static_cast<_Up&&>(__f)
 	      ? weak_ordering::equivalent
 	      : static_cast<_Tp&&>(__e) < static_cast<_Up&&>(__f)
@@ -827,18 +820,16 @@ namespace std
 	}
 
     public:
-      template<typename _Tp, typename _Up>
+      template<typename _Tp, __decayed_same_as<_Tp> _Up>
 	requires __partially_ordered<_Tp, _Up> || __op_eq_lt<_Tp, _Up>
-	constexpr decltype(auto)
+	constexpr partial_ordering
 	operator()(_Tp&& __e, _Up&& __f) const
 	noexcept(_S_noexcept<_Tp, _Up>())
 	{
-	  static_assert(same_as<decay_t<_Tp>, decay_t<_Up>>);
-
 	  if constexpr (__partially_ordered<_Tp, _Up>)
 	    return _Partial_order{}(static_cast<_Tp&&>(__e),
 				    static_cast<_Up&&>(__f));
-	  else if constexpr (__op_eq_lt<_Tp, _Up>)
+	  else // __op_eq_lt<_Tp, _Up>
 	    return static_cast<_Tp&&>(__e) == static_cast<_Up&&>(__f)
 	      ? partial_ordering::equivalent
 	      : static_cast<_Tp&&>(__e) < static_cast<_Up&&>(__f)
diff --git a/libstdc++-v3/testsuite/18_support/comparisons/algorithms/fallback.cc b/libstdc++-v3/testsuite/18_support/comparisons/algorithms/fallback.cc
new file mode 100644
index 00000000000..ae458528f17
--- /dev/null
+++ b/libstdc++-v3/testsuite/18_support/comparisons/algorithms/fallback.cc
@@ -0,0 +1,42 @@
+// { dg-options "-std=gnu++20" }
+// { dg-do compile { target c++20 } }
+
+#include <compare>
+
+using std::strong_ordering;
+using std::partial_ordering;
+
+namespace adl
+{
+  struct S { };
+  void strong_ordering(const S&, const S&);
+  bool operator==(const S&, S&) { return true; }
+  bool operator<(const S&, S&) { return true; }
+}
+
+template<typename T, typename U>
+  concept has_strong_order_fallback = requires (T& t, U& u) {
+    std::compare_strong_order_fallback(t, u);
+  };
+
+template<typename T, typename U>
+  concept has_weak_order_fallback = requires (T& t, U& u) {
+    std::compare_weak_order_fallback(t, u);
+  };
+
+template<typename T, typename U>
+  concept has_partial_order_fallback = requires (T& t, U& u) {
+    std::compare_partial_order_fallback(t, u);
+  };
+
+using adl::S;
+
+static_assert( has_strong_order_fallback<S, S> );
+static_assert( has_strong_order_fallback<const S, S> );
+static_assert( ! has_strong_order_fallback<const S, const S> );
+static_assert( has_weak_order_fallback<S, S> );
+static_assert( has_weak_order_fallback<const S, S> );
+static_assert( ! has_weak_order_fallback<const S, const S> );
+static_assert( has_partial_order_fallback<S, S> );
+static_assert( has_partial_order_fallback<const S, S> );
+static_assert( ! has_partial_order_fallback<const S, const S> );
