diff --git a/AABB_tree/doc/AABB_tree/Concepts/AABBGeomTraits.h b/AABB_tree/doc/AABB_tree/Concepts/AABBGeomTraits.h
index 577bad2f6f7..7d2c7313812 100644
--- a/AABB_tree/doc/AABB_tree/Concepts/AABBGeomTraits.h
+++ b/AABB_tree/doc/AABB_tree/Concepts/AABBGeomTraits.h
@@ -37,12 +37,12 @@ among `Ray_3`, `Segment_3`, `Line_3`, `Triangle_3`, `Plane_3` and `Bbox_3`. Rele
 typedef Hidden_type Do_intersect_3; 
 
 /*! 
-A functor object to construct the intersection between two geometric objects. 
-Provides the nested type `Result<A, B>` where `Result<A, B>::Type` is the return 
-type of the `operator()(A, B)`.
+A functor object to construct the intersection between two geometric objects.
+This functor must support the result_of protocol, that is the return 
+type of the `operator()(A, B)` is `CGAL::cpp11::result<Intersect_3(A,B)>`.
 
 Provides the operators: 
-`Result<A, B>::type operator()(const A& a, const B& b);` 
+`CGAL::cpp11::result<Intersect_3(A,B)> operator()(const A& a, const B& b);` 
 where `A` and `B` are any relevant types among `Ray_3`, `Segment_3`, `Line_3`, 
 `Triangle_3`, `Plane_3` and `Bbox_3`. 
 Relevant herein means that a line primitive (ray, segment, line) is tested 
diff --git a/AABB_tree/doc/AABB_tree/Concepts/AABBTraits.h b/AABB_tree/doc/AABB_tree/Concepts/AABBTraits.h
index 7252f1c06cf..2d892f36bb0 100644
--- a/AABB_tree/doc/AABB_tree/Concepts/AABBTraits.h
+++ b/AABB_tree/doc/AABB_tree/Concepts/AABBTraits.h
@@ -58,12 +58,10 @@ typedef std::pair<Point_3, Primitive::Id> Point_and_primitive_id;
 typedef std::pair<Object, Primitive::Id> Object_and_primitive_id;
 
 
-  /*!  A nested class template to aquire the pair of the return type of
-intersections with an object of type `Query` and a
-`Primitive::Id` through the member typedef `Type`.
-
-This class is convertible to `Point_and_primitive_id`.
-  */
+/*!  A nested class template providing as a pair the intersection result of a `Query` object
+and a `Primitive::Datum`, together with the `Primitive::Id` of the primitive intersected.
+The type of the pair is given by the nested type `Type`.
+*/
 
   template <typename Query>
   struct Intersection_and_primitive_id{};
@@ -123,7 +121,9 @@ typedef Hidden_type Do_intersect;
 
 /*! 
 A functor object to compute the intersection of a query and a primitive. Provides the operator: 
-`boost::optional<Intersection_and_primitive_id<Query>::type operator()(const Query & q, const Primitive& primitive);` which returns the intersection as a pair composed of an object and a primitive id, iff the query intersects the primitive. 
+`boost::optional<Intersection_and_primitive_id<Query>::type > operator()(const Query & q, const Primitive& primitive);` which returns the intersection as a pair composed of an object and a primitive id, iff the query intersects the primitive. 
+\cgalHeading{Note on Backward Compatibility}
+Before the release 4.3 of \cgal, the return type of this function used to be `boost::optional<Object_and_primitive_id>`.
 */ 
 typedef Hidden_type Intersect; 
 
diff --git a/AABB_tree/include/CGAL/AABB_traits.h b/AABB_tree/include/CGAL/AABB_traits.h
index d6e1f2ac335..02fd3e968a0 100644
--- a/AABB_tree/include/CGAL/AABB_traits.h
+++ b/AABB_tree/include/CGAL/AABB_traits.h
@@ -68,6 +68,7 @@ public:
 
   typedef typename std::pair<typename GeomTraits::Point_3, typename Primitive::Id> Point_and_primitive_id;
 
+  ///\todo update this to use the return type of `GeomTraits::Intersection` together with an helper to remove optional
   template<typename Query>
   struct Intersection_and_primitive_id {
     typedef std::pair< 
diff --git a/AABB_tree/include/CGAL/AABB_tree.h b/AABB_tree/include/CGAL/AABB_tree.h
index ce637c52880..6405e38f18b 100644
--- a/AABB_tree/include/CGAL/AABB_tree.h
+++ b/AABB_tree/include/CGAL/AABB_tree.h
@@ -87,17 +87,12 @@ namespace CGAL {
     /// \deprecated 
 		typedef typename AABBTraits::Object_and_primitive_id Object_and_primitive_id;
 
-    /*!  
-\todo Fill in the types in the std::pair.
-A nested type to aquire the  return type of intersections
-with an object of type `Query` through the member typedef
-`Type` equal to `std::pair< >`
+    /*!
+    An alias to AABBTraits::Interesction_and_primitive_id
     */
-
     template<typename Query>
     struct Intersection_and_primitive_id {
       typedef typename AABBTraits::template Intersection_and_primitive_id<Query>::Type Type;
-      typedef Type type;
     };
 
     
@@ -246,7 +241,7 @@ public:
     /// `Intersection_and_primitive_id<Query>::Type`,
     /// between the query and the input data to
     /// the iterator. `do_intersect()`
-    /// predicates and intersections must be defined for Query`
+    /// predicates and intersections must be defined for `Query`
     /// in the `AABBTraits` class.
 		template<typename Query, typename OutputIterator>
 		OutputIterator all_intersections(const Query& query, OutputIterator out) const;