diff --git a/Surface_reconstruction_points_3/include/CGAL/Mesh_3/Refine_tets.h b/Surface_reconstruction_points_3/include/CGAL/Mesh_3/Poisson_refine_cells_3.h
similarity index 83%
rename from Surface_reconstruction_points_3/include/CGAL/Mesh_3/Refine_tets.h
rename to Surface_reconstruction_points_3/include/CGAL/Mesh_3/Poisson_refine_cells_3.h
index 698e13c47a5..e3a48fc7d85 100644
--- a/Surface_reconstruction_points_3/include/CGAL/Mesh_3/Refine_tets.h
+++ b/Surface_reconstruction_points_3/include/CGAL/Mesh_3/Poisson_refine_cells_3.h
@@ -17,8 +17,8 @@
 //
 // Author(s)     : Laurent RINEAU
 
-#ifndef CGAL_MESH_3_REFINE_TETS_H
-#define CGAL_MESH_3_REFINE_TETS_H
+#ifndef CGAL_MESH_3_POISSON_REFINE_CELLS_3_H
+#define CGAL_MESH_3_POISSON_REFINE_CELLS_3_H
 
 #include <CGAL/Mesher_level.h>
 #include <CGAL/Meshes/Triangulation_mesher_level_traits_3.h>
@@ -40,9 +40,9 @@ template <class Tr,
           class Container =
           Meshes::Double_map_container<
             typename Tr::Cell_handle,
-            typename Criteria::Quality>
+            typename Criteria::Cell_quality>
           >
-class Refine_tets_base :
+class Poisson_refine_tets_base :
     public Container,
     public Triangulation_mesher_level_traits_3<Tr>,
     public No_test_point_conflict
@@ -63,14 +63,14 @@ protected:
   typedef typename Tr::Facet Facet;
 
 public:
-  typedef typename Criteria::Quality Quality;
+  typedef typename Criteria::Cell_quality Cell_quality;
 
   using Triangulation_mesher_level_traits_3<Tr>::triangulation_ref_impl;
 
 public:
   /** \name CONSTRUCTORS */
 
-  Refine_tets_base(Tr& t, Criteria crit) 
+  Poisson_refine_tets_base(Tr& t, Criteria crit) 
     : Triangulation_mesher_level_traits_3<Tr>(t), criteria(crit) {}
 
 protected:
@@ -81,20 +81,20 @@ protected:
 protected:
   /* --- protected functions --- */
 
-  bool should_be_refined(const Cell_handle c, Quality& qual) const
+  bool should_be_refined(const Cell_handle c, Cell_quality& qual) const
   {
     return criteria.is_bad_object()(c,qual);
   }
 
   bool should_be_refined(const Cell_handle c) const
   {
-    Quality q;
+    Cell_quality q;
     return should_be_refined(c, q);
   }
 
   bool test_if_cell_is_bad(const Cell_handle c)
   {
-    Quality q;
+    Cell_quality q;
     if( c->is_in_domain() && should_be_refined(c, q) )
       {
 	this->add_bad_element(c, q);
@@ -137,7 +137,7 @@ public:
 #if CGAL_MESH_3_DEBUG_BEFORE_CONFLICTS
   void before_conflicts_impl(const Cell_handle&, const Point& p)
   {
-    std::cerr << "Refine_tets: before conflicts of " << p;
+    std::cerr << "Poisson_refine_tets: before conflicts of " << p;
   }
 #else
   void before_conflicts_impl(const Cell_handle&, const Point&)
@@ -152,7 +152,7 @@ public:
     std::cerr << "  REJECTED!" << std::endl;
 #endif
   }
-}; // end Refine_tets_base  
+}; // end Poisson_refine_tets_base  
 
 template <class Tr,
           class Criteria,
@@ -160,16 +160,16 @@ template <class Tr,
           class Oracle,
           class Container = Meshes::Double_map_container<
             typename Tr::Cell_handle,
-            typename Criteria::Quality>
+            typename Criteria::Cell_quality>
 >
-class Refine_tets_with_oracle_base 
-  : public Refine_tets_base<Tr,
+class Poisson_refine_tets_with_oracle_base 
+  : public Poisson_refine_tets_base<Tr,
                             Criteria,
                             Container>
 {
 public:
-  typedef Refine_tets_base<Tr, Criteria, Container> Base;
-  typedef Refine_tets_with_oracle_base<Tr, 
+  typedef Poisson_refine_tets_base<Tr, Criteria, Container> Base;
+  typedef Poisson_refine_tets_with_oracle_base<Tr, 
                                        Criteria,
                                        Surface,
                                        Oracle,
@@ -186,7 +186,7 @@ public:
 
   /** \name CONSTRUCTORS */
 
-  Refine_tets_with_oracle_base(Tr& t, Criteria crit, Surface& s, Oracle& o)
+  Poisson_refine_tets_with_oracle_base(Tr& t, Criteria crit, Surface& s, Oracle& o)
     : Base(t, crit), surface(s), oracle(o) {}
 
 public:
@@ -198,7 +198,7 @@ public:
 #ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
     // Check if triangulation's geometric traits provides a robust circumcenter computation
     if (triangulation_ref_impl().side_of_sphere(c, p, true) != ON_BOUNDED_SIDE)
-      std::cerr << "Refine_tets_with_oracle_base::conflicts_zone_impl: ERROR: circumcenter out of sphere!\n";
+      std::cerr << "Poisson_refine_tets_with_oracle_base::conflicts_zone_impl: ERROR: circumcenter out of sphere!\n";
 #endif
 
     zone.cell = c;
@@ -263,21 +263,21 @@ protected:
   Surface& surface;
   Oracle& oracle;
 
-}; // end Refine_tets_with_oracle_base
+}; // end Poisson_refine_tets_with_oracle_base
 
 template <typename Tr,
           typename Criteria,
           typename Surface,
           typename Oracle, // BEURK
           typename BaseP = // workaround for VC7, see below
-             Refine_tets_with_oracle_base<Tr, Criteria, Surface, Oracle>,
+             Poisson_refine_tets_with_oracle_base<Tr, Criteria, Surface, Oracle>,
           typename Facets_level = Refine_facets<Tr>
  >
-class Refine_tets : 
+class Poisson_refine_tets : 
   public BaseP, 
   public Mesher_level <
     Tr,
-    Refine_tets<Tr, Criteria, Surface, Oracle, BaseP, Facets_level>,
+    Poisson_refine_tets<Tr, Criteria, Surface, Oracle, BaseP, Facets_level>,
     typename Tr::Cell_handle,
     Facets_level,
     Triangulation_mesher_level_traits_3<Tr>
@@ -287,16 +287,16 @@ class Refine_tets :
 
   Facets_level& facets_level;
 public:
-  typedef Refine_tets<Tr, Criteria, Surface, Oracle, Base, Facets_level> Self;
+  typedef Poisson_refine_tets<Tr, Criteria, Surface, Oracle, Base, Facets_level> Self;
   typedef Mesher_level <
     Tr,
-    Refine_tets<Tr, Criteria, Surface, Oracle, Base, Facets_level>,
+    Poisson_refine_tets<Tr, Criteria, Surface, Oracle, Base, Facets_level>,
     typename Tr::Cell_handle,
     Facets_level,
     Triangulation_mesher_level_traits_3<Tr>
   > Mesher;
   
-  Refine_tets(Tr& t, Criteria crit, Surface& surface, Oracle& oracle, Facets_level& facets_level)
+  Poisson_refine_tets(Tr& t, Criteria crit, Surface& surface, Oracle& oracle, Facets_level& facets_level)
     : Base(t, crit, surface, oracle), Mesher(facets_level), facets_level(facets_level)
   {} // here VC7 complain about default constructor of Base, if the
      // workaround is not used.
@@ -315,9 +315,9 @@ public:
     return s.str();
   }
 
-}; // end class Refine_tets
+}; // end class Poisson_refine_tets
 
 }; // end namespace Mesh_3
 }; // end namespace CGAL
 
-#endif // CGAL_MESH_3_REFINE_TETS_H
+#endif // CGAL_MESH_3_POISSON_REFINE_CELLS_3_H
diff --git a/Surface_reconstruction_points_3/include/CGAL/Mesh_criteria_3.h b/Surface_reconstruction_points_3/include/CGAL/Poisson_mesh_cell_criteria_3.h
similarity index 85%
rename from Surface_reconstruction_points_3/include/CGAL/Mesh_criteria_3.h
rename to Surface_reconstruction_points_3/include/CGAL/Poisson_mesh_cell_criteria_3.h
index dd583fae500..9e9f2d0be2d 100644
--- a/Surface_reconstruction_points_3/include/CGAL/Mesh_criteria_3.h
+++ b/Surface_reconstruction_points_3/include/CGAL/Poisson_mesh_cell_criteria_3.h
@@ -17,41 +17,32 @@
 //
 // Author(s)     : Laurent RINEAU
 
-#ifndef CGAL_MESH_CRITERIA_3_H
-#define CGAL_MESH_CRITERIA_3_H
+#ifndef CGAL_POISSON_MESH_CRITERIA_3_H
+#define CGAL_POISSON_MESH_CRITERIA_3_H
 
 #include <iostream>
 
 namespace CGAL {
 
-template <typename Tr>
-class Mesh_criteria_3 
+template <class Tr>
+class Poisson_mesh_cell_criteria_3 
 {
   double squared_radius_bound_;
   double radius_edge_bound_;
 public:
-  typedef typename Tr::Cell_handle Cell_handle;
-
-  Mesh_criteria_3(const double radius_edge_bound = 2, //< radius edge ratio bound (ignored if zero)
-		  const double radius_bound = 0) //< cell radius bound (ignored if zero)
-    : squared_radius_bound_(radius_bound*radius_bound),
-      radius_edge_bound_(radius_edge_bound)
-  {
-  };
-
-  struct Quality : public std::pair<double, double>
+  struct Cell_quality : public std::pair<double, double>
   {
     typedef std::pair<double, double> Base;
 
-    Quality() : Base() {};
-    Quality(double _aspect, double _sq_size) : Base(_aspect, _sq_size) {};
+    Cell_quality() : Base() {};
+    Cell_quality(double _aspect, double _sq_size) : Base(_aspect, _sq_size) {};
 
     const double& sq_size() const { return second; }
     const double& aspect() const { return first; }
 
     // q1<q2 means q1 is prioritised over q2
     // ( q1 == *this, q2 == q )
-    bool operator<(const Quality& q) const
+    bool operator<(const Cell_quality& q) const
     {
       if( sq_size() > 1 )
 	if( q.sq_size() > 1 )
@@ -71,6 +62,15 @@ public:
     return squared_radius_bound_; 
   };
 
+  typedef typename Tr::Cell_handle Cell_handle;
+
+  Poisson_mesh_cell_criteria_3(const double radius_edge_bound = 2, //< radius edge ratio bound (ignored if zero)
+		  const double radius_bound = 0) //< cell radius bound (ignored if zero)
+    : squared_radius_bound_(radius_bound*radius_bound),
+      radius_edge_bound_(radius_edge_bound)
+  {
+  };
+
   inline 
   void set_squared_radius_bound(const double squared_radius_bound) 
   { 
@@ -103,7 +103,7 @@ public:
 	squared_radius_bound_(squared_radius_bound) {};
       
     bool operator()(const Cell_handle& c,
-                    Quality& qual) const
+                    Cell_quality& qual) const
     {
       const Point_3& p = c->vertex(0)->point();
       const Point_3& q = c->vertex(1)->point();
@@ -133,7 +133,7 @@ public:
         }
       if( radius_edge_bound_ == 0 )
 	{
-	  qual = Quality(0,1);
+	  qual = Cell_quality(0,1);
 	  return false;
 	}
 
@@ -155,15 +155,15 @@ public:
   Is_bad is_bad_object() const
   { return Is_bad(radius_edge_bound_, squared_radius_bound_); }
 
-}; // end Mesh_criteria_3
+}; // end Poisson_mesh_cell_criteria_3
 
   template <typename Tr>
   std::ostream& operator<<(std::ostream& os,
-                           const typename Mesh_criteria_3<Tr>::Quality& q)
+                           const typename Poisson_mesh_cell_criteria_3<Tr>::Cell_quality& q)
   {
     return os << q.sq_size() << ", " << q.aspect();
   }
 
 } // end namespace CGAL
 
-#endif // CGAL_MESH_CRITERIA_3_H
+#endif // CGAL_POISSON_MESH_CRITERIA_3_H
diff --git a/Surface_reconstruction_points_3/include/CGAL/Poisson_reconstruction_function.h b/Surface_reconstruction_points_3/include/CGAL/Poisson_reconstruction_function.h
index 3fa33bb1202..7ab894384cc 100644
--- a/Surface_reconstruction_points_3/include/CGAL/Poisson_reconstruction_function.h
+++ b/Surface_reconstruction_points_3/include/CGAL/Poisson_reconstruction_function.h
@@ -282,8 +282,8 @@ private:
     CGAL_TRACE("Calls delaunay_refinement(radius_edge_ratio_bound=%lf, cell_radius_bound=%lf, max_vertices=%u, enlarge_ratio=%lf)\n",
                radius_edge_ratio_bound, cell_radius_bound, max_vertices, enlarge_ratio);
 
-    Sphere enlarged_bbox = enlarged_bounding_sphere(enlarge_ratio);
-    unsigned int nb_vertices_added = poisson_refine_triangulation(*m_tr,radius_edge_ratio_bound,cell_radius_bound,max_vertices,enlarged_bbox);
+    Sphere elarged_bsphere = enlarged_bounding_sphere(enlarge_ratio);
+    unsigned int nb_vertices_added = poisson_refine_triangulation(*m_tr,radius_edge_ratio_bound,cell_radius_bound,max_vertices,elarged_bsphere);
 
     CGAL_TRACE("End of delaunay_refinement()\n");
 
diff --git a/Surface_reconstruction_points_3/include/CGAL/poisson_refine_triangulation.h b/Surface_reconstruction_points_3/include/CGAL/poisson_refine_triangulation.h
index 6c7846a2bb0..08b76cc0b71 100644
--- a/Surface_reconstruction_points_3/include/CGAL/poisson_refine_triangulation.h
+++ b/Surface_reconstruction_points_3/include/CGAL/poisson_refine_triangulation.h
@@ -21,8 +21,8 @@
 
 // CGAL
 #include <CGAL/Mesher_level.h>
-#include <CGAL/Mesh_3/Refine_tets.h>
-#include <CGAL/Mesh_criteria_3.h>
+#include <CGAL/Mesh_3/Poisson_refine_cells_3.h>
+#include <CGAL/Poisson_mesh_cell_criteria_3.h>
 #include <CGAL/surface_reconstruction_points_assertions.h>
 
 CGAL_BEGIN_NAMESPACE
@@ -39,12 +39,12 @@ template <class Tr,
           class Surface,
           class Oracle,
           class Container = Meshes::Double_map_container<typename Tr::Cell_handle,
-                                                         typename Criteria::Quality>
+                                                         typename Criteria::Cell_quality>
 >
 class Poisson_mesher_level_impl_base :
-    public Mesh_3::Refine_tets_with_oracle_base<Tr, Criteria, Surface, Oracle, Container>
+    public Mesh_3::Poisson_refine_tets_with_oracle_base<Tr, Criteria, Surface, Oracle, Container>
 {
-  typedef Mesh_3::Refine_tets_with_oracle_base<Tr, Criteria, Surface, Oracle, Container> Base;
+  typedef Mesh_3::Poisson_refine_tets_with_oracle_base<Tr, Criteria, Surface, Oracle, Container> Base;
 
 public:
   // Inherited methods and fields used below
@@ -56,7 +56,7 @@ public:
   typedef typename Tr::Vertex_handle Vertex_handle;
   typedef typename Tr::Cell_handle Cell_handle;
   typedef typename Tr::Point Point;
-  typedef typename Base::Quality Quality;
+  typedef typename Base::Cell_quality Cell_quality;
 
 public:
   /** \name CONSTRUCTORS */
@@ -73,7 +73,7 @@ protected:
 
   bool test_if_cell_is_bad(const Cell_handle c)
   {
-    Quality q;
+    Cell_quality q;
     if( is_in_domain(c) && should_be_refined(c, q) )
     {
       this->add_bad_element(c, q);
@@ -218,7 +218,7 @@ unsigned int poisson_refine_triangulation(
   typedef typename Gt::Point_3 Point;
 
   // Mesher_level types
-  typedef Mesh_criteria_3<Tr> Tets_criteria;
+  typedef Poisson_mesh_cell_criteria_3<Tr> Tets_criteria;
   typedef typename CGAL::Surface_mesh_traits_generator_3<Surface>::type Oracle;
   typedef Poisson_mesher_level<Tr, Tets_criteria, Surface, Oracle, Null_mesher_level> Refiner;