diff --git a/Octree/include/CGAL/Octree.h b/Octree/include/CGAL/Octree.h
index 64f186c06ef..cd3d26b4dd7 100644
--- a/Octree/include/CGAL/Octree.h
+++ b/Octree/include/CGAL/Octree.h
@@ -23,8 +23,7 @@
 #define CGAL_OCTREE_3_H
 
 #include <CGAL/Octree/Octree_node.h>
-#include <CGAL/Octree/Criterion.h>
-#include <CGAL/Octree/IO.h>
+#include <CGAL/Octree/Stop_criterion.h>
 
 #include <CGAL/bounding_box.h>
 #include <boost/iterator/transform_iterator.hpp>
@@ -129,7 +128,7 @@ namespace CGAL {
       m_root.unsplit();
     }
 
-    void refine(std::function<bool(Node *)> stop_criterion) {
+    void refine(std::function<bool(const Node *)> stop_criterion) {
 
       // create a side length map
       for (int i = 0; i <= (int) 10; i++)
@@ -164,47 +163,8 @@ namespace CGAL {
       }
     }
 
-    void refine(size_t max_depth, size_t max_pts_num) {
-
-      refine([&](Node *n) -> bool {
-        return (n->num_points() <= max_pts_num || n->depth() == max_depth);
-      });
-
-      /*
-
-      // create a side length map
-      for (int i = 0; i <= (int) 10; i++)
-        m_side_per_depth.push_back(m_bbox_side / (FT) (1 << i));
-
-      // Initialize a queue of nodes that need to be refined
-      std::queue<Node*> todo;
-      todo.push(&m_root);
-
-      // Process items in the queue until it's consumed fully
-      while (!todo.empty()) {
-
-        // Get the next element
-        auto current = todo.front();
-        todo.pop();
-        int depth = current->depth();
-
-        // Check if this node needs to be processed
-        if (current->num_points() > max_pts_num && current->depth() < max_depth) {
-
-          // Split this node
-          current->split();
-
-          // Redistribute its points
-          reassign_points((*current));
-
-          // Process each of its children
-          for (int i = 0; i < 8; ++i)
-            todo.push(&(*current)[i]);
-
-        }
-      }
-
-       */
+    void refine(size_t max_depth, size_t bucket_size) {
+      refine(Stop_at_max_depth_or_bucket_size(max_depth, bucket_size));
     }
 
     Node &root() { return m_root; }
@@ -223,7 +183,6 @@ namespace CGAL {
 
       // If all else is equal, recursively compare the trees themselves
       return rhs.m_root == m_root;
-
     }
 
 
diff --git a/Octree/include/CGAL/Octree/Criterion.h b/Octree/include/CGAL/Octree/Criterion.h
deleted file mode 100644
index 2f6b84d5240..00000000000
--- a/Octree/include/CGAL/Octree/Criterion.h
+++ /dev/null
@@ -1,64 +0,0 @@
-
-#ifndef OCTREE_CRITERION_H
-#define OCTREE_CRITERION_H
-
-#include <CGAL/Octree.h>
-#include <CGAL/Octree/Octree_node.h>
-
-
-// Possible criterions
-template <class Node>
-struct Stop_at_max_depth {
-
-  std::size_t max_depth;
-
-  Stop_at_max_depth(std::size_t max_depth) : max_depth(max_depth) {}
-
-  bool operator()(Node n) const {
-    return n->depth() == max_depth; // not sure you can know that from node only,
-    // otherwise your criterion could also take a
-    // reference to the full octree as parameter
-  }
-};
-
- /*
-
-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 {
-  Normal_map normal_map;
-  FT max_dev;
-
-  Stop_at_normal_deviation(Normal_map normal_map,
-                           FT max_dev)
-          : normal_map(normal_map), max_dev(max_dev) {}
-
-  bool operator()(const Node &n) const {
-    FT dev = 0;
-
-    for (Iterator it = n.begin(); it != n.end(); ++it)
-      dev += compute_deviation(get(normal_map, *it)); // whatever compute_deviation is :)
-
-    // if your node defines begin() and end(), you can also use a C++11 loop:
-    // for (const Range_type& r : n)
-    //   dev += compute_deviation(get (normal_map, r));
-
-    return dev < max_dev;
-  }
-};
-
-*/
-
-#endif //OCTREE_CRITERION_H
diff --git a/Octree/include/CGAL/Octree/Stop_criterion.h b/Octree/include/CGAL/Octree/Stop_criterion.h
new file mode 100644
index 00000000000..42410e41bfe
--- /dev/null
+++ b/Octree/include/CGAL/Octree/Stop_criterion.h
@@ -0,0 +1,74 @@
+
+#ifndef OCTREE_STOP_CRITERION_H
+#define OCTREE_STOP_CRITERION_H
+
+namespace CGAL {
+
+  struct Stop_at_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) :
+            m_max_depth(max_depth), m_bucket_size(bucket_size) {}
+
+    template<class Node>
+    bool operator()(Node n) const {
+      return (n->num_points() <= m_bucket_size || n->depth() == m_max_depth);
+    }
+  };
+
+  struct Stop_at_max_depth {
+
+    std::size_t m_max_depth;
+
+    Stop_at_max_depth(std::size_t max_depth) : m_max_depth(max_depth) {}
+
+    template<class Node>
+    bool operator()(Node n) const {
+      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 {
+ Normal_map normal_map;
+ FT max_dev;
+
+ Stop_at_normal_deviation(Normal_map normal_map,
+                          FT max_dev)
+         : normal_map(normal_map), max_dev(max_dev) {}
+
+ bool operator()(const Node &n) const {
+   FT dev = 0;
+
+   for (Iterator it = n.begin(); it != n.end(); ++it)
+     dev += compute_deviation(get(normal_map, *it)); // whatever compute_deviation is :)
+
+   // if your node defines begin() and end(), you can also use a C++11 loop:
+   // for (const Range_type& r : n)
+   //   dev += compute_deviation(get (normal_map, r));
+
+   return dev < max_dev;
+ }
+};
+
+*/
+
+#endif //OCTREE_STOP_CRITERION_H