diff --git a/src/core/include/mp_units/bits/quantity_cast.h b/src/core/include/mp_units/bits/quantity_cast.h
index 70ae64af..11a19d39 100644
--- a/src/core/include/mp_units/bits/quantity_cast.h
+++ b/src/core/include/mp_units/bits/quantity_cast.h
@@ -55,11 +55,11 @@ class quantity;
  *
  * @tparam ToQS a quantity specification to use for a target quantity
  */
-template<QuantitySpec auto ToQS, Quantity Q>
-  requires(interconvertible(ToQS, get_quantity_spec(Q::reference)))
+template<QuantitySpec auto ToQS, typename Q>
+  requires Quantity<std::remove_cvref_t<Q>> && castable_to(get_quantity_spec(Q::reference), ToQS)
 [[nodiscard]] constexpr Quantity auto quantity_cast(Q&& q)
 {
-  constexpr reference<ToQS, Q::unit> r;
+  constexpr reference<ToQS, std::remove_cvref_t<Q>::unit> r;
   return std::forward<Q>(q).number() * r;
 }
 
diff --git a/src/core/include/mp_units/bits/quantity_concepts.h b/src/core/include/mp_units/bits/quantity_concepts.h
index 3dcc06bc..726aa87c 100644
--- a/src/core/include/mp_units/bits/quantity_concepts.h
+++ b/src/core/include/mp_units/bits/quantity_concepts.h
@@ -54,21 +54,9 @@ concept Quantity = requires(T* t) { detail::to_base_specialization_of_quantity(t
  * the provided dimension/reference type.
  */
 template<typename Q, auto V>
-concept QuantityOf = Quantity<Q> && ((Dimension<std::remove_const_t<decltype(V)>> && Q::dimension == V) ||
-                                     (QuantitySpec<std::remove_const_t<decltype(V)>> && Q::quantity_spec == V) ||
-                                     (Reference<std::remove_const_t<decltype(V)>> && Q::reference == V));
-
-/**
- * @brief A concept matching all quantities with provided dimension or reference
- *
- * Satisfied by all quantities with a dimension/reference being the instantiation derived from
- * the provided dimension/reference type.
- */
-template<typename Q, auto V>
-concept WeakQuantityOf =
+concept QuantityOf =
   Quantity<Q> && ((Dimension<std::remove_const_t<decltype(V)>> && Q::dimension == V) ||
-                  (QuantitySpec<std::remove_const_t<decltype(V)>> && interconvertible(Q::quantity_spec, V)) ||
-                  (Reference<std::remove_const_t<decltype(V)>> && Q::dimension == V.dimension && Q::unit == V.unit));
+                  (QuantitySpec<std::remove_const_t<decltype(V)>> && implicitly_convertible_to(Q::quantity_spec, V)));
 
 /**
  * @brief A concept matching all external quantities like types
diff --git a/src/core/include/mp_units/bits/quantity_point_concepts.h b/src/core/include/mp_units/bits/quantity_point_concepts.h
index fd18ea65..9dd36192 100644
--- a/src/core/include/mp_units/bits/quantity_point_concepts.h
+++ b/src/core/include/mp_units/bits/quantity_point_concepts.h
@@ -95,8 +95,7 @@ template<typename QP, auto V>
 concept QuantityPointOf =
   QuantityPoint<QP> &&
   ((Dimension<std::remove_const_t<decltype(V)>> && QP::dimension == V) ||
-   (QuantitySpec<std::remove_const_t<decltype(V)>> && QP::quantity_spec == V) ||
-   (Reference<std::remove_const_t<decltype(V)>> && QP::reference == V) ||
+   (QuantitySpec<std::remove_const_t<decltype(V)>> && implicitly_convertible_to(QP::quantity_spec, V)) ||
    (PointOrigin<std::remove_const_t<decltype(V)>> &&
     std::same_as<std::remove_const_t<decltype(QP::absolute_point_origin)>, std::remove_const_t<decltype(V)>>));
 
diff --git a/src/core/include/mp_units/bits/sudo_cast.h b/src/core/include/mp_units/bits/sudo_cast.h
index 5e01a99b..2bc3bee0 100644
--- a/src/core/include/mp_units/bits/sudo_cast.h
+++ b/src/core/include/mp_units/bits/sudo_cast.h
@@ -43,7 +43,7 @@ namespace detail {
  * @tparam To a target quantity type to cast to
  */
 template<Quantity To, auto R, typename Rep>
-  requires(interconvertible(To::reference, R)) &&
+  requires(castable_to(get_quantity_spec(R), To::quantity_spec)) &&
           ((get_unit(R) == To::unit && std::constructible_from<typename To::rep, Rep>) ||
            (get_unit(R) != To::unit))  // && scalable_with_<typename To::rep>))
 // TODO how to constrain the second part here?
diff --git a/src/core/include/mp_units/reference.h b/src/core/include/mp_units/reference.h
index f316c126..84821698 100644
--- a/src/core/include/mp_units/reference.h
+++ b/src/core/include/mp_units/reference.h
@@ -122,19 +122,19 @@ struct reference {
   template<auto Q2, auto U2>
   [[nodiscard]] friend consteval bool convertible_to(reference, reference<Q2, U2>)
   {
-    return convertible_to(Q, Q2) && convertible_to(U, U2);
+    return implicitly_convertible_to(Q, Q2) && convertible_to(U, U2);
   }
 
   template<AssociatedUnit U2>
   [[nodiscard]] friend consteval bool convertible_to(reference, U2 u2)
   {
-    return convertible_to(Q, get_quantity_spec(u2)) && convertible_to(U, u2);
+    return implicitly_convertible_to(Q, get_quantity_spec(u2)) && convertible_to(U, u2);
   }
 
   template<AssociatedUnit U1>
   [[nodiscard]] friend consteval bool convertible_to(U1 u1, reference)
   {
-    return convertible_to(get_quantity_spec(u1), Q) && convertible_to(u1, U);
+    return implicitly_convertible_to(get_quantity_spec(u1), Q) && convertible_to(u1, U);
   }
 };