diff --git a/docs/spec/ProFacade.md b/docs/spec/ProFacade.md
index 1ca2515..3730e15 100644
--- a/docs/spec/ProFacade.md
+++ b/docs/spec/ProFacade.md
@@ -12,7 +12,7 @@ A type `F` meets the *ProFacade* requirements of a type `P` if `F` meets the [*P
 | `F::relocatability`            | A [core constant expression](https://en.cppreference.com/w/cpp/language/constant_expression) of type [`constraint_level`](constraint_level.md) that defines the required relocatability of `P`. |
 | `F::destructibility`           | A [core constant expression](https://en.cppreference.com/w/cpp/language/constant_expression) of type [`constraint_level`](constraint_level.md) that defines the required destructibility of `P`. |
 
-*Since 4.0.2*: `P` shall be a pointer-like type eligible for `proxy`. A type `P` is eligible if `P` is not a specialization of `proxy` and the following condition is satisfied:
+*Since 4.0.2*: `P` shall be a pointer-like type eligible for `proxy`. A type `P` is eligible if the following condition is satisfied:
 
 ```cpp
 (requires { *std::declval<P&>(); } || requires { typename P::element_type; }) &&
diff --git a/docs/spec/proxy/assignment.md b/docs/spec/proxy/assignment.md
index d3558bc..8934ce1 100644
--- a/docs/spec/proxy/assignment.md
+++ b/docs/spec/proxy/assignment.md
@@ -38,7 +38,7 @@ Assigns a new value to `proxy` or destroys the contained value.
 - `(1)` Destroys the current contained value if it exists. After the call, `*this` does not contain a value.
 - `(2)` Copy assignment operator copies the contained value of `rhs` to `*this`. If `rhs` does not contain a value, it destroys the contained value of `*this` (if any) as if by `auto(rhs).swap(*this)`. The copy assignment is trivial when `F::copyability == constraint_level::trivial` is `true`.
 - `(3)` Move assignment operator moves the contained value of `rhs` to `*this`. If `rhs` does not contain a value, it destroys the contained value of `*this` (if any). If the move construction throws when `F::relocatability == constraint_level::nontrivial`, `*this` does not contain a value. After move assignment, `rhs` is in a valid state with an unspecified value. The move assignment operator does not participate in overload resolution when `F::copyability == constraint_level::trivial`, falling back to the trivial copy assignment operator.
-- `(4)` Let `VP` be `std::decay_t<P>`. Sets the contained value to an object of type `VP`, direct-non-list-initialized with `std::forward<P>(ptr)`. Participates in overload resolution only if `VP` is a pointer-like type eligible for `proxy` (see [*ProFacade* requirements](../ProFacade.md)). *Since 3.3.0*: If [`proxiable<VP, F>`](../proxiable.md) is `false`, the program is ill-formed and a diagnostic is generated.
+- `(4)` Let `VP` be `std::decay_t<P>`. Sets the contained value to an object of type `VP`, direct-non-list-initialized with `std::forward<P>(ptr)`. Participates in overload resolution only if `VP` is not a specialization of `proxy` and is a pointer-like type eligible for `proxy` (see [*ProFacade* requirements](../ProFacade.md)). *Since 3.3.0*: If [`proxiable<VP, F>`](../proxiable.md) is `false`, the program is ill-formed and a diagnostic is generated.
 
 ## Return Value
 
diff --git a/docs/spec/proxy/constructor.md b/docs/spec/proxy/constructor.md
index 61f9182..922bf8f 100644
--- a/docs/spec/proxy/constructor.md
+++ b/docs/spec/proxy/constructor.md
@@ -44,7 +44,7 @@ Creates a new `proxy`.
 - `(1)` Default constructor and the constructor taking `nullptr` construct a `proxy` that does not contain a value.
 - `(2)` Copy constructor constructs a `proxy` whose contained value is that of `rhs` if `rhs` contains a value, or otherwise, constructs a `proxy` that does not contain a value. As per the `requires` clause, the copy constructor is trivial when `F::copyability == constraint_level::trivial`.
 - `(3)` Move constructor constructs a `proxy` whose contained value is that of `rhs` if `rhs` contains a value, or otherwise, constructs a `proxy` that does not contain a value. `rhs` is in a valid but unspecified state after move construction. As per the `requires` clause, the move constructor does not participate in overload resolution when `F::copyability == constraint_level::trivial`, so that a move construction falls back to the trivial copy constructor.
-- `(4)` Let `VP` be `std::decay_t<P>`. Constructs a `proxy` whose contained value is of type `VP`, direct-non-list-initialized with `std::forward<P>(ptr)`. Participates in overload resolution only if `VP` is a pointer-like type eligible for `proxy` (see [*ProFacade* requirements](../ProFacade.md)).
+- `(4)` Let `VP` be `std::decay_t<P>`. Constructs a `proxy` whose contained value is of type `VP`, direct-non-list-initialized with `std::forward<P>(ptr)`. Participates in overload resolution only if `VP` is not a specialization of `proxy` and is a pointer-like type eligible for `proxy` (see [*ProFacade* requirements](../ProFacade.md)).
 - `(5)` Constructs a `proxy` whose contained value is of type `P`, direct-non-list-initialized with `std::forward<Args>(args)...`. Participates in overload resolution only if `P` is a pointer-like type eligible for `proxy`.
 - `(6)` Constructs a `proxy` whose contained value is of type `P`, direct-non-list-initialized with `il, std::forward<Args>(args)...`. Participates in overload resolution only if `P` is a pointer-like type eligible for `proxy`.
 
diff --git a/include/proxy/v4/proxy.h b/include/proxy/v4/proxy.h
index a3a1d9b..ecf5c78 100644
--- a/include/proxy/v4/proxy.h
+++ b/include/proxy/v4/proxy.h
@@ -635,16 +635,17 @@ struct refl_accessor_traits<R, F, true>
 template <class R, class F, bool IsDirect>
 using refl_accessor_t = typename refl_accessor_traits<R, F, IsDirect>::type;
 
-template <class P>
-struct ptr_traits : inapplicable_traits {};
-template <class P>
-  requires((
-               requires { *std::declval<P&>(); } ||
-               requires { typename P::element_type; }) &&
-           requires { typename std::pointer_traits<P>::element_type; })
-struct ptr_traits<P> : applicable_traits {};
-template <class F>
-struct ptr_traits<proxy<F>> : inapplicable_traits {};
+template <class T>
+concept pointer_like = (requires { *std::declval<T&>(); } ||
+    requires { typename T::element_type; }) &&
+    requires { typename std::pointer_traits<T>::element_type; };
+
+template <class T, template <class...> class TT>
+struct specialization_traits : inapplicable_traits {};
+template <template <class...> class TT, class... Args>
+struct specialization_traits<TT<Args...>, TT> : applicable_traits {};
+template <class T, template <class...> class TT>
+concept specialization_of = specialization_traits<T, TT>::applicable;
 
 template <class P, class F, std::size_t ActualSize, std::size_t MaxSize>
 consteval bool diagnose_proxiable_size_too_large() {
@@ -912,7 +913,7 @@ add_qualifier_t<proxy<F>, Q>
 } // namespace details
 
 template <class P, class F>
-concept proxiable = facade<F> && details::ptr_traits<P>::applicable &&
+concept proxiable = facade<F> && details::pointer_like<P> &&
                     details::facade_traits<F>::template applicable_ptr<P>;
 
 template <facade F>
@@ -990,7 +991,8 @@ class proxy : public details::facade_traits<F>::direct_accessor,
   template <class P>
   constexpr proxy(P&& ptr) noexcept(
       std::is_nothrow_constructible_v<std::decay_t<P>, P>)
-    requires(details::ptr_traits<std::decay_t<P>>::applicable &&
+    requires(!details::specialization_of<std::decay_t<P>, proxy> &&
+             details::pointer_like<std::decay_t<P>> &&
              std::is_constructible_v<std::decay_t<P>, P>)
   {
     initialize<std::decay_t<P>>(std::forward<P>(ptr));
@@ -998,8 +1000,7 @@ class proxy : public details::facade_traits<F>::direct_accessor,
   template <class P, class... Args>
   constexpr explicit proxy(std::in_place_type_t<P>, Args&&... args) noexcept(
       std::is_nothrow_constructible_v<P, Args...>)
-    requires(details::ptr_traits<P>::applicable &&
-             std::is_constructible_v<P, Args...>)
+    requires(details::pointer_like<P> && std::is_constructible_v<P, Args...>)
   {
     initialize<P>(std::forward<Args>(args)...);
   }
@@ -1009,7 +1010,7 @@ class proxy : public details::facade_traits<F>::direct_accessor,
       Args&&... args) noexcept(std::
                                    is_nothrow_constructible_v<
                                        P, std::initializer_list<U>&, Args...>)
-    requires(details::ptr_traits<P>::applicable &&
+    requires(details::pointer_like<P> &&
              std::is_constructible_v<P, std::initializer_list<U>&, Args...>)
   {
     initialize<P>(il, std::forward<Args>(args)...);
@@ -1060,7 +1061,8 @@ class proxy : public details::facade_traits<F>::direct_accessor,
   constexpr proxy& operator=(P&& ptr) noexcept(
       std::is_nothrow_constructible_v<std::decay_t<P>, P> &&
       F::destructibility >= constraint_level::nothrow)
-    requires(details::ptr_traits<std::decay_t<P>>::applicable &&
+    requires(!details::specialization_of<std::decay_t<P>, proxy> &&
+             details::pointer_like<std::decay_t<P>> &&
              std::is_constructible_v<std::decay_t<P>, P> &&
              F::destructibility >= constraint_level::nontrivial)
   {
@@ -1127,8 +1129,7 @@ class proxy : public details::facade_traits<F>::direct_accessor,
   constexpr P& emplace(Args&&... args) noexcept(
       std::is_nothrow_constructible_v<P, Args...> &&
       F::destructibility >= constraint_level::nothrow)
-    requires(details::ptr_traits<P>::applicable &&
-             std::is_constructible_v<P, Args...> &&
+    requires(details::pointer_like<P> && std::is_constructible_v<P, Args...> &&
              F::destructibility >= constraint_level::nontrivial)
   {
     reset();
@@ -1138,7 +1139,7 @@ class proxy : public details::facade_traits<F>::direct_accessor,
   constexpr P& emplace(std::initializer_list<U> il, Args&&... args) noexcept(
       std::is_nothrow_constructible_v<P, std::initializer_list<U>&, Args...> &&
       F::destructibility >= constraint_level::nothrow)
-    requires(details::ptr_traits<P>::applicable &&
+    requires(details::pointer_like<P> &&
              std::is_constructible_v<P, std::initializer_list<U>&, Args...> &&
              F::destructibility >= constraint_level::nontrivial)
   {
@@ -1146,7 +1147,9 @@ class proxy : public details::facade_traits<F>::direct_accessor,
     return initialize<P>(il, std::forward<Args>(args)...);
   }
 
-  friend void swap(proxy& lhs, proxy& rhs) noexcept(noexcept(lhs.swap(rhs))) {
+  friend void swap(proxy& lhs, proxy& rhs) noexcept(noexcept(lhs.swap(rhs)))
+    requires(requires { lhs.swap(rhs); })
+  {
     lhs.swap(rhs);
   }
   friend bool operator==(const proxy& lhs, std::nullptr_t) noexcept {
@@ -1163,7 +1166,7 @@ class proxy : public details::facade_traits<F>::direct_accessor,
     return details::invoke_impl<F, true, D, O>(p, std::forward<Args>(args)...);
   }
   template <class D, class O, class... Args>
-  friend auto invoke(proxy<F>&& p, Args&&... args) ->
+  friend auto invoke(proxy&& p, Args&&... args) ->
       typename details::overload_traits<O>::return_type {
     return details::invoke_impl<F, true, D, O>(std::move(p),
                                                std::forward<Args>(args)...);
diff --git a/tests/proxy_traits_tests.cpp b/tests/proxy_traits_tests.cpp
index 0f092e6..ab593bd 100644
--- a/tests/proxy_traits_tests.cpp
+++ b/tests/proxy_traits_tests.cpp
@@ -498,4 +498,7 @@ static_assert(!std::is_constructible_v<pro::proxy<DefaultFacade>,
                                        ProxyWrapperTemplate<void>>);
 static_assert(std::is_move_constructible_v<ProxyWrapperTemplate<void>>);
 
+// proxiable shall not reject a specialization of proxy.
+static_assert(pro::proxiable<pro::proxy_view<DefaultFacade>, DefaultFacade>);
+
 } // namespace proxy_traits_tests_details