diff --git a/AABB_tree/doc_tex/AABB_tree_ref/AABBGeomTraits.tex b/AABB_tree/doc_tex/AABB_tree_ref/AABBGeomTraits.tex
index d2d2d8950bc..d62186becf8 100644
--- a/AABB_tree/doc_tex/AABB_tree_ref/AABBGeomTraits.tex
+++ b/AABB_tree/doc_tex/AABB_tree_ref/AABBGeomTraits.tex
@@ -57,7 +57,7 @@ Any instantiation of \ccc{CGAL::Kernel} is a model of this traits concept.
 
 \ccSeeAlso
 
-\ccc{AABB_traits<GeomTraits,TrianglePrimitive>}.
+\ccc{AABB_traits<GeomTraits,AABBPrimitive>}.
 
 \end{ccRefConcept}
 
diff --git a/AABB_tree/doc_tex/AABB_tree_ref/AABBTraits.tex b/AABB_tree/doc_tex/AABB_tree_ref/AABBTraits.tex
index 0c9de047327..3cc8e19c4b4 100644
--- a/AABB_tree/doc_tex/AABB_tree_ref/AABBTraits.tex
+++ b/AABB_tree/doc_tex/AABB_tree_ref/AABBTraits.tex
@@ -28,8 +28,7 @@ The concept \ccRefName\ provides the geometric primitive types and methods for t
 
 \ccTypes
 
-\ccNestedType{Primitive}{This type must be a model of the concept
-\ccc{AABBPrimitive}.}
+\ccNestedType{Primitive}{Type of primitive. Must be a model of the concept \ccc{AABBPrimitive}.}
 \ccGlue
 \ccNestedType{Bounding_box}{Bounding box type.}
 \ccGlue
@@ -41,7 +40,7 @@ The following types are required for projection queries.
 \ccGlue
 \ccNestedType{Projection_query}{Type for which projection queries are issued.}
 \ccGlue
-\ccNestedType{Projection}{Type of projection output.}
+\ccNestedType{Projection}{Type of projection result.}
 	
 
 \ccCreation
@@ -54,14 +53,14 @@ The following types are required for projection queries.
 During the construction of the \ccc{AABB_tree}, the primitives are sorted according to some comparison functions related to the $x$, $y$ or $z$ coordinate axis.
 
 % TODO: replace by sort function (way much faster as we do not have to sort many times)
-\ccMethod{bool x_less_than(const Primitive & pr1, const Primitive & pr2);}{}
+\ccMethod{bool less_x(const Primitive & pr1, const Primitive & pr2);}{}
 \ccGlue
-\ccMethod{bool y_less_than(const Primitive & pr1, const Primitive & pr2);}{}
+\ccMethod{bool less_y(const Primitive & pr1, const Primitive & pr2);}{}
 \ccGlue
-\ccMethod{bool z_less_than(const Primitive & pr1, const Primitive & pr2);}{}
+\ccMethod{bool less_z(const Primitive & pr1, const Primitive & pr2);}{}
 
 \ccMethod{Bounding_box compute_bbox(const_primitive_iterator begin,                                                const_primitive_iterator beyond);}
-{Computes and returns the bounding box of a set of primitives.}
+{Returns the bounding box of a set of primitives.}
 
 The following predicates are required for each type \ccc{Query}
 for which the class \ccc{AABB_tree<Traits>} may receive a query.
diff --git a/AABB_tree/include/CGAL/AABB_traits.h b/AABB_tree/include/CGAL/AABB_traits.h
index bf6c69f9ec7..aa27d4628ec 100644
--- a/AABB_tree/include/CGAL/AABB_traits.h
+++ b/AABB_tree/include/CGAL/AABB_traits.h
@@ -80,11 +80,11 @@ public:
   ~AABB_traits() { };
 
   /// Comparison functions
-  static bool x_less_than(const Primitive& pr1, const Primitive& pr2)
+  static bool less_x(const Primitive& pr1, const Primitive& pr2)
   { return pr1.reference_point().x() < pr2.reference_point().x(); }
-  static bool y_less_than(const Primitive& pr1, const Primitive& pr2)
+  static bool less_y(const Primitive& pr1, const Primitive& pr2)
   { return pr1.reference_point().y() < pr2.reference_point().y(); }
-  static bool z_less_than(const Primitive& pr1, const Primitive& pr2)
+  static bool less_z(const Primitive& pr1, const Primitive& pr2)
   { return pr1.reference_point().z() < pr2.reference_point().z(); }
 
   /// UNDOCUMENTED FEATURE
@@ -182,13 +182,13 @@ AABB_traits<GT,P>::sort_primitives(PrimitiveIterator first,
   switch(longest_axis(bbox))
   {
   case CGAL_AXIS_X: // sort along x
-    std::nth_element(first, middle, beyond, x_less_than);
+    std::nth_element(first, middle, beyond, less_x);
     break;
   case CGAL_AXIS_Y: // sort along y
-    std::nth_element(first, middle, beyond, y_less_than);
+    std::nth_element(first, middle, beyond, less_y);
     break;
   case CGAL_AXIS_Z: // sort along z
-    std::nth_element(first, middle, beyond, z_less_than);
+    std::nth_element(first, middle, beyond, less_z);
     break;
   default:
     CGAL_error();