diff --git a/AABB_tree/include/CGAL/AABB_traits.h b/AABB_tree/include/CGAL/AABB_traits.h
index 7b4d6d9f25f..f098a934259 100644
--- a/AABB_tree/include/CGAL/AABB_traits.h
+++ b/AABB_tree/include/CGAL/AABB_traits.h
@@ -53,7 +53,7 @@ public:
   typedef typename GeomTraits::Point_3::Point Point;
 #endif
 
-  typedef typename std::pair<typename Point, typename primitive> Point_and_primitive;
+  typedef typename std::pair<typename Point, typename Primitive> Point_and_primitive;
 
   // types for search tree
   // TOFIX: how can we avoid repeating those?
diff --git a/AABB_tree/include/CGAL/AABB_tree.h b/AABB_tree/include/CGAL/AABB_tree.h
index 8f9f4fc1489..f2917ff9caa 100644
--- a/AABB_tree/include/CGAL/AABB_tree.h
+++ b/AABB_tree/include/CGAL/AABB_tree.h
@@ -104,7 +104,7 @@ namespace CGAL {
 
         template<typename Query>
         bool any_intersection(const Query& q,
-                              Intersection& intersection) const;
+                              Point_and_primitive& intersection) const;
 
         template<typename Query, typename OutputIterator>
         bool any_intersected_primitive(const Query& q,
@@ -113,22 +113,25 @@ namespace CGAL {
         // distance queries
         FT squared_distance(const Point& q, const Point& hint) const;
         FT squared_distance(const Point& q) const;
-        Point closest_point(const Point& q, const Point& hint) const;
-        Point closest_point(const Point& q) const;
+        Point closest_point(const Point& q, const Point& hint);
+        Point closest_point(const Point& q);
         Primitive closest_primitive(const Point& q, const Point& hint) const;
         Primitive closest_primitive(const Point& q) const;
         Point_and_primitive closest_point_and_primitive(const Point& q, const Point& hint) const;
         Point_and_primitive closest_point_and_primitive(const Point& q) const;
 
         Bounding_box root_bbox() const { return m_p_root->bounding_box(); }
-        bool is_empty() const { return m_data.empty(); }
+        bool empty() const { return m_data.empty(); }
         size_t size() const { return m_data.size(); }
 
         /// generic traversal of tree
         template <class Query, class Traversal_traits>
         void traversal(const Query& q, Traversal_traits& traits) const
         {
-            m_p_root->template traversal<Traversal_traits,Query>(q, traits, m_data.size());
+            if(!empty())
+                m_p_root->template traversal<Traversal_traits,Query>(q, traits, m_data.size());
+            else
+                std::cerr << "AABB tree traversal with empty tree" << std::endl;
         }
         //////////////////////////////////////////////
 
@@ -197,7 +200,7 @@ namespace CGAL {
                 return AABBTraits().do_intersect(q, node.bounding_box());
             }
 
-            int intersection_number() const { return m_nb_intersections; }
+            int number_of_intersections() const { return m_nb_intersections; }
 
         private:
             Point_and_primitive m_intersection;
@@ -232,8 +235,8 @@ namespace CGAL {
             }
 
         private:
-            Intersection m_intersection;
             Output_iterator m_out_it;
+            Point_and_primitive m_intersection;
         };
 
 
@@ -284,7 +287,7 @@ namespace CGAL {
             {
                 // TOFIX: update m_closest_primitive
                 m_closest_point = AABBTraits().nearest_point(query, primitive, m_closest_point);
-                m_sphere = AABBTraits().sphere(q, m_closest_point);
+                m_sphere = AABBTraits().sphere(query, m_closest_point);
             }
 
             bool do_intersect(const Point& q, const Node& node) const
@@ -422,7 +425,7 @@ namespace CGAL {
         Traversal_traits traversal_traits;
 
         this->traversal(query, traversal_traits);
-        return traversal_traits.intersection_number();
+        return traversal_traits.number_of_intersections();
     }
 
 
@@ -492,18 +495,18 @@ namespace CGAL {
     template<typename Tr>
     typename AABB_tree<Tr>::Point
         AABB_tree<Tr>::closest_point(const Point& query,
-                                     const Point& hint) const
+                                     const Point& hint) 
     {
-        Distance_traits traversal_traits(query,hint);
-        this->traversal(query, traversal_traits);
-        return traversal_traits.projection();
+        Distance_traits distance_traits(query,hint);
+        this->traversal(query, distance_traits);
+        return distance_traits.closest_point();
     }
 
     // closest point without hint, the search KD-tree is queried for the
     // first nearest neighbor point to get a hint
     template<typename Tr>
     typename AABB_tree<Tr>::Point
-        AABB_tree<Tr>::closest_point(const Point& query) const
+        AABB_tree<Tr>::closest_point(const Point& query) 
     {
         // construct search KD-tree if needed
         Point hint;
diff --git a/AABB_tree/test/AABB_tree/aabb_intersection_triangle_test.cpp b/AABB_tree/test/AABB_tree/aabb_intersection_triangle_test.cpp
index c091afaf66a..c4e4ebada5e 100644
--- a/AABB_tree/test/AABB_tree/aabb_intersection_triangle_test.cpp
+++ b/AABB_tree/test/AABB_tree/aabb_intersection_triangle_test.cpp
@@ -51,7 +51,7 @@ void test_all_query_types(Tree& tree)
     typedef typename K::Vector_3 Vector;
     typedef typename K::Segment_3 Segment;
     typedef typename Tree::Primitive Primitive;
-    typedef typename Tree::Intersection Intersection;
+    typedef typename Tree::Point_and_primitive Point_and_primitive;
 
     Point p((FT)-0.5, (FT)-0.5, (FT)-0.5);
     Point q((FT) 0.5, (FT) 0.5, (FT) 0.5);
@@ -77,13 +77,13 @@ void test_all_query_types(Tree& tree)
     tree.all_intersected_primitives(segment,std::back_inserter(primitives));
 
     // any_intersection
-    Intersection intersection;
+    Point_and_primitive intersection;
     success = tree.any_intersection(ray,intersection);
     success = tree.any_intersection(line,intersection);
     success = tree.any_intersection(segment,intersection);
 
     // all_intersections
-    std::list<Intersection> intersections;
+    std::list<Point_and_primitive> intersections;
     tree.all_intersections(ray,std::back_inserter(intersections));
     tree.all_intersections(line,std::back_inserter(intersections));
     tree.all_intersections(segment,std::back_inserter(intersections));