diff --git a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h
index 9d855d66792..25fdd4e2441 100644
--- a/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h
+++ b/Point_set_shape_detection_3/include/CGAL/Shape_detection_3/Octree.h
@@ -277,11 +277,22 @@ namespace CGAL {
       // | 3.| 2.|
       // +---+---+
       // z max before z min, then y max before y min, then x max before x min
-      void createTree() {
+      void createTree(double cluster_epsilon_for_max_level_recomputation = -1.) {
         buildBoundingCube();
         std::size_t count = 0;
         m_max_level = 0;
 
+        if (cluster_epsilon_for_max_level_recomputation > 0.)
+        {
+          FT bbox_diagonal = (FT) CGAL::sqrt(
+            (m_bBox.xmax() - m_bBox.xmin()) * (m_bBox.xmax() - m_bBox.xmin())
+            + (m_bBox.ymax() - m_bBox.ymin()) * (m_bBox.ymax() - m_bBox.ymin()) 
+            + (m_bBox.zmax() - m_bBox.zmin()) * (m_bBox.zmax() - m_bBox.zmin()));
+
+          m_set_max_level = std::size_t (std::log2 (bbox_diagonal
+                                                    / cluster_epsilon_for_max_level_recomputation));
+        }
+
         std::stack<Cell *> stack;
         m_root = new Cell(0, this->size() - 1, m_center, 0);
         stack.push(m_root);