diff --git a/adoc/chapters/programming_interface.adoc b/adoc/chapters/programming_interface.adoc
index 56945638..3167379d 100644
--- a/adoc/chapters/programming_interface.adoc
+++ b/adoc/chapters/programming_interface.adoc
@@ -9822,12 +9822,6 @@ bool operator>=(std::nullptr_t, const multi_ptr& rhs)
 The following is the overview of the legacy interface from 1.2.1 provided
 for the [code]#multi_ptr# class.
 
-This legacy class supports the deprecated [code]#address_space::constant_space#
-address space, which can be used to represent a pointer to <<constant-memory>>.
-Pointers to <<constant-memory>> have an implementation-defined address space,
-and each implementation can define whether it is legal to assign such a pointer
-to a generic address pointer.
-
 [source,,linenums]
 ----
 include::{header_dir}/multipointerlegacy.h[lines=4..-1]
diff --git a/adoc/headers/multipointer.h b/adoc/headers/multipointer.h
index 944d4d9e..3d42f53f 100644
--- a/adoc/headers/multipointer.h
+++ b/adoc/headers/multipointer.h
@@ -88,6 +88,15 @@ class multi_ptr {
   multi_ptr(
       accessor<AccDataT, Dimensions, Mode, target::local, IsPlaceholder>);
 
+  // Deprecated
+  // Available only when:
+  //   Space == access::address_space::constant_space &&
+  //   (std::is_same_v<std::remove_const_t<ElementType>, std::remove_const_t<AccDataT>>) &&
+  //   (std::is_const_v<ElementType> || !std::is_const_v<AccDataT>)
+  template <typename AccDataT, int Dimensions, access::placeholder IsPlaceholder>
+  multi_ptr(
+      accessor<AccDataT, Dimensions, access_mode::read, target::constant_buffer, IsPlaceholder>);
+
   // Assignment and access operators
   multi_ptr& operator=(const multi_ptr&);
   multi_ptr& operator=(multi_ptr&&);
@@ -296,6 +305,14 @@ class multi_ptr<VoidType, Space, DecorateAddress> {
   multi_ptr(
       accessor<ElementType, Dimensions, Mode, target::local, IsPlaceholder>);
 
+  // Deprecated
+  // Available only when:
+  //   Space == access::address_space::constant_space &&
+  //   (std::is_const_v<VoidType> || !std::is_const_v<ElementType>)
+  template <typename ElementType, int Dimensions, access::placeholder IsPlaceholder>
+  multi_ptr(
+      accessor<ElementType, Dimensions, access_mode::read, target::constant_buffer, IsPlaceholder>);
+
   // Assignment operators
   multi_ptr& operator=(const multi_ptr&);
   multi_ptr& operator=(multi_ptr&&);
@@ -304,7 +321,7 @@ class multi_ptr<VoidType, Space, DecorateAddress> {
   pointer get() const;
 
   // Conversion to the underlying pointer type
-  explicit operator pointer() const;
+  operator pointer() const;
 
   // Explicit conversion to a multi_ptr<ElementType>
   // Available only when: (std::is_const_v<ElementType> || !std::is_const_v<VoidType>)
@@ -384,6 +401,14 @@ template <typename T, int Dimensions, access::placeholder IsPlaceholder>
 multi_ptr(accessor<T, Dimensions, access_mode::read_write, target::device, IsPlaceholder>)
     -> multi_ptr<T, access::address_space::global_space, access::decorated::no>;
 
+template <typename T, int Dimensions, access::placeholder IsPlaceholder>
+multi_ptr(accessor<T, Dimensions, access_mode::read, target::constant_buffer, IsPlaceholder>)
+    -> multi_ptr<const T, access::address_space::constant_space, access::decorated::no>;
+
+template <typename T, int Dimensions, access_mode Mode, access::placeholder IsPlaceholder>
+multi_ptr(accessor<T, Dimensions, Mode, target::local, IsPlaceholder>)
+    -> multi_ptr<T, access::address_space::local_space, access::decorated::no>;
+
 template <typename T, int Dimensions>
 multi_ptr(local_accessor<T, Dimensions>)
     -> multi_ptr<T, access::address_space::local_space, access::decorated::no>;
diff --git a/adoc/headers/multipointerlegacy.h b/adoc/headers/multipointerlegacy.h
index 2fdb6a9c..08bad414 100644
--- a/adoc/headers/multipointerlegacy.h
+++ b/adoc/headers/multipointerlegacy.h
@@ -43,16 +43,34 @@ class [[deprecated]] multi_ptr<ElementType, Space, access::decorated::legacy> {
   }
   ElementType* operator->() const;
 
-  // Only if Space == global_space
+  // Available only when:
+  //   (Space == access::address_space::global_space ||
+  //    Space == access::address_space::generic_space) &&
+  //   (std::is_same_v<std::remove_const_t<ElementType>, std::remove_const_t<AccDataT>>) &&
+  //   (std::is_const_v<ElementType> ||
+  //    !std::is_const_v<accessor<AccDataT, Dimensions, Mode, target::device,
+  //                              IsPlaceholder>::value_type>)
   template <int Dimensions, access_mode Mode, access::placeholder IsPlaceholder>
   multi_ptr(
       accessor<ElementType, Dimensions, Mode, target::device, IsPlaceholder>);
 
-  // Only if Space == local_space
+  // Available only when:
+  //   (Space == access::address_space::local_space ||
+  //    Space == access::address_space::generic_space) &&
+  //   (std::is_same_v<std::remove_const_t<ElementType>, std::remove_const_t<AccDataT>>) &&
+  //   (std::is_const_v<ElementType> || !std::is_const_v<AccDataT>)
   template <int Dimensions, access_mode Mode, access::placeholder IsPlaceholder>
   multi_ptr(
       accessor<ElementType, Dimensions, Mode, target::local, IsPlaceholder>);
 
+  // Available only when:
+  //   (Space == access::address_space::local_space ||
+  //    Space == access::address_space::generic_space) &&
+  //   (std::is_same_v<std::remove_const_t<ElementType>, std::remove_const_t<AccDataT>>) &&
+  //   (std::is_const_v<ElementType> || !std::is_const_v<AccDataT>)
+  template <typename AccDataT, int Dimensions>
+  multi_ptr(local_accessor<AccDataT, Dimensions>);
+
   // Only if Space == constant_space
   template <int Dimensions, access_mode Mode, access::placeholder IsPlaceholder>
   multi_ptr(accessor<ElementType, Dimensions, Mode, target::constant_buffer,
@@ -69,11 +87,11 @@ class [[deprecated]] multi_ptr<ElementType, Space, access::decorated::legacy> {
   operator ElementType*() const;
 
   // Implicit conversion to a multi_ptr<void>
-  // Only available when ElementType is not const-qualified
+  // Available only when ElementType is not const-qualified
   operator multi_ptr<void, Space, access::decorated::legacy>() const;
 
   // Implicit conversion to a multi_ptr<const void>
-  // Only available when ElementType is const-qualified
+  // Available only when ElementType is const-qualified
   operator multi_ptr<const void, Space, access::decorated::legacy>() const;
 
   // Implicit conversion to multi_ptr<const ElementType, Space>
@@ -176,15 +194,30 @@ class [[deprecated]] multi_ptr<VoidType, Space, access::decorated::legacy> {
   multi_ptr& operator=(VoidType*);
   multi_ptr& operator=(std::nullptr_t);
 
-  // Only if Space == global_space
+  // Available only when:
+  //   (Space == access::address_space::global_space ||
+  //    Space == access::address_space::generic_space) &&
+  //   (std::is_const_v<VoidType> ||
+  //    !std::is_const_v<accessor<ElementType, Dimensions, Mode, target::device,
+  //                              IsPlaceholder>::value_type>)
   template <typename ElementType, int Dimensions, access_mode Mode>
   multi_ptr(accessor<ElementType, Dimensions, Mode, target::device>);
 
-  // Only if Space == local_space
+  // Available only when:
+  //   (Space == access::address_space::local_space ||
+  //    Space == access::address_space::generic_space) &&
+  //   (std::is_const_v<VoidType> || !std::is_const_v<ElementType>)
   template <typename ElementType, int Dimensions, access_mode Mode>
   multi_ptr(accessor<ElementType, Dimensions, Mode, target::local>);
 
-  // Only if Space == constant_space
+  // Available only when:
+  //   (Space == access::address_space::local_space ||
+  //    Space == access::address_space::generic_space) &&
+  //   (std::is_const_v<VoidType> || !std::is_const_v<ElementType>)
+  template <typename AccDataT, int Dimensions>
+  multi_ptr(local_accessor<AccDataT, Dimensions>);
+
+  // Only if Space == access::address_space::constant_space
   template <typename ElementType, int Dimensions, access_mode Mode>
   multi_ptr(accessor<ElementType, Dimensions, Mode, target::constant_buffer>);