diff --git a/Octree/include/CGAL/Octree.h b/Octree/include/CGAL/Octree.h
index 9fc9b2171a1..cb84b76fe94 100644
--- a/Octree/include/CGAL/Octree.h
+++ b/Octree/include/CGAL/Octree.h
@@ -23,7 +23,7 @@
 #define CGAL_OCTREE_3_H
 
 #include <CGAL/Octree/Octree_node.h>
-#include <CGAL/Octree/Stop_criterion.h>
+#include <CGAL/Octree/Split_criterion.h>
 
 #include <CGAL/bounding_box.h>
 #include <boost/iterator/transform_iterator.hpp>
@@ -128,7 +128,7 @@ namespace CGAL {
       m_root.unsplit();
     }
 
-    void refine(std::function<bool(const Node &)> stop_criterion) {
+    void refine(std::function<bool(const Node &)> split_criterion) {
 
       // create a side length map
       for (int i = 0; i <= (int) 10; i++)
@@ -147,7 +147,7 @@ namespace CGAL {
         int depth = current->depth();
 
         // Check if this node needs to be processed
-        if (!stop_criterion(*current)) {
+        if (split_criterion(*current)) {
 
           // Split this node
           current->split();
@@ -164,7 +164,7 @@ namespace CGAL {
     }
 
     void refine(size_t max_depth, size_t bucket_size) {
-      refine(Stop_at_max_depth_or_bucket_size(max_depth, bucket_size));
+      refine(Split_to_max_depth_or_bucket_size(max_depth, bucket_size));
     }
 
     Node &root() { return m_root; }
diff --git a/Octree/include/CGAL/Octree/Stop_criterion.h b/Octree/include/CGAL/Octree/Split_criterion.h
similarity index 58%
rename from Octree/include/CGAL/Octree/Stop_criterion.h
rename to Octree/include/CGAL/Octree/Split_criterion.h
index 3d6f709f8f7..ebd07ce14b5 100644
--- a/Octree/include/CGAL/Octree/Stop_criterion.h
+++ b/Octree/include/CGAL/Octree/Split_criterion.h
@@ -1,50 +1,39 @@
 
-#ifndef OCTREE_STOP_CRITERION_H
-#define OCTREE_STOP_CRITERION_H
+#ifndef OCTREE_SPLIT_CRITERION_H
+#define OCTREE_SPLIT_CRITERION_H
+
+#include <iostream>
 
 namespace CGAL {
 
-  struct Stop_at_max_depth_or_bucket_size {
+  struct Split_to_max_depth_or_bucket_size {
 
     std::size_t m_max_depth, m_bucket_size;
 
-    Stop_at_max_depth_or_bucket_size(std::size_t max_depth, std::size_t bucket_size) :
+    Split_to_max_depth_or_bucket_size(std::size_t max_depth, std::size_t bucket_size) :
             m_max_depth(max_depth), m_bucket_size(bucket_size) {}
 
     template<class Node>
     bool operator()(const Node &n) const {
-      return (n.num_points() <= m_bucket_size || n.depth() == m_max_depth);
+      return (n.num_points() > m_bucket_size && n.depth() < m_max_depth);
     }
   };
 
-  struct Stop_at_max_depth {
+  struct Split_to_max_depth {
 
     std::size_t m_max_depth;
 
-    Stop_at_max_depth(std::size_t max_depth) : m_max_depth(max_depth) {}
+    Split_to_max_depth(std::size_t max_depth) : m_max_depth(max_depth) {}
 
     template<class Node>
     bool operator()(const Node &n) const {
-      return n.depth() == m_max_depth;
+      return n.depth() < m_max_depth;
     }
   };
-
 }
 
 /*
 
-struct Stop_at_max_number_of_points {
- std::size_t max_nb_points;
-
- Stop_at_max_number_of_points(const std::size_t &max_nb_points)
-         : max_nb_points(max_nb_points) {}
-
- bool operator()(const Node &n) const {
-   return n.number_of_points() // internally, the node can use std::distance(begin, end)
-          < max_nb_points;
- }
-};
-
 // Just for an example using outside info (like a normal map)
 // The normals remain unknown to the octree but are used for construction
 struct Stop_at_normal_deviation {
@@ -71,4 +60,4 @@ struct Stop_at_normal_deviation {
 
 */
 
-#endif //OCTREE_STOP_CRITERION_H
+#endif //OCTREE_SPLIT_CRITERION_H