diff --git a/Orthtree/include/CGAL/Orthtree.h b/Orthtree/include/CGAL/Orthtree.h
index 7abd20858ff..89b5eabd9f9 100644
--- a/Orthtree/include/CGAL/Orthtree.h
+++ b/Orthtree/include/CGAL/Orthtree.h
@@ -248,7 +248,7 @@ public:
     // save orthtree attributes
     m_bbox_min = construct_point_d_from_array(bbox_min);
     m_side_per_depth.push_back(bbox_max[0] - bbox_min[0]);
-    points(root()) = m_traits.root_node_contents();
+    data(root()) = m_traits.root_node_contents();
   }
 
   /// @}
@@ -699,11 +699,11 @@ public:
     return m_node_depths[n];
   }
 
-  Node_data& points(Node_index n) {
+  Node_data& data(Node_index n) {
     return m_node_points[n];
   }
 
-  const Node_data& points(Node_index n) const {
+  const Node_data& data(Node_index n) const {
     return m_node_points[n];
   }
 
@@ -841,7 +841,6 @@ public:
 
     // Add the node's points to its children
     m_traits.distribute_node_contents(n, *this, center);
-    //reassign_points(n, points(n).begin(), points(n).end(), center);
   }
 
   /*!
@@ -1038,7 +1037,7 @@ private: // functions :
 
       // Loop through each of the points contained by the node
       // Note: there might be none, and that should be fine!
-      for (auto p: points(node)) {
+      for (auto p: data(node)) {
 
         // Pair that point with its distance from the search point
         Node_element_with_distance current_point_with_distance =
diff --git a/Orthtree/include/CGAL/Orthtree/IO.h b/Orthtree/include/CGAL/Orthtree/IO.h
index 58155fefb06..1bf6bdd7143 100644
--- a/Orthtree/include/CGAL/Orthtree/IO.h
+++ b/Orthtree/include/CGAL/Orthtree/IO.h
@@ -47,7 +47,7 @@ std::ostream& print_orthtree_node(std::ostream& os, const Node_index& node, cons
      << ") ";
 
   os << "("
-     << tree.points(node).size()
+     << tree.data(node).size()
      << ") ";
 
   // If a node is a leaf, mark it
diff --git a/Orthtree/include/CGAL/Orthtree/Split_predicates.h b/Orthtree/include/CGAL/Orthtree/Split_predicates.h
index 766a76e3570..b1a38ee1c22 100644
--- a/Orthtree/include/CGAL/Orthtree/Split_predicates.h
+++ b/Orthtree/include/CGAL/Orthtree/Split_predicates.h
@@ -51,7 +51,7 @@ public:
    */
   template<typename Node_index, typename Tree>
   bool operator()(Node_index i, const Tree &tree) const {
-    return (tree.points(i).size() > m_bucket_size);
+    return (tree.data(i).size() > m_bucket_size);
   }
 
 };
@@ -132,7 +132,7 @@ public:
    */
   template<typename Node_index, typename Tree>
   bool operator()(Node_index i, const Tree &tree) const {
-    std::size_t num_points = tree.points(i).size();
+    std::size_t num_points = tree.data(i).size();
     std::size_t depth = tree.depth(i);
     return (num_points > m_bucket_size && depth < m_max_depth);
   }
diff --git a/Orthtree/include/CGAL/Orthtree_traits_point_2.h b/Orthtree/include/CGAL/Orthtree_traits_point_2.h
index 96940dc0276..ff4030a8510 100644
--- a/Orthtree/include/CGAL/Orthtree_traits_point_2.h
+++ b/Orthtree/include/CGAL/Orthtree_traits_point_2.h
@@ -185,7 +185,7 @@ public:
   template <typename Node_index, typename Tree>
   void distribute_node_contents(Node_index n, Tree& tree, const Point_d& center) {
     CGAL_precondition(!tree.is_leaf(n));
-    reassign_points(n, tree, center, tree.points(n));
+    reassign_points(n, tree, center, tree.data(n));
   }
 
   Point_d get_element(const Node_data_element& index) const {
@@ -207,7 +207,7 @@ private:
 
     // Root case: reached the last dimension
     if (dimension == Dimension::value) {
-      tree.points(tree.child(n, coord.to_ulong())) = points;
+      tree.data(tree.child(n, coord.to_ulong())) = points;
       return;
     }
 
diff --git a/Orthtree/include/CGAL/Orthtree_traits_point_3.h b/Orthtree/include/CGAL/Orthtree_traits_point_3.h
index 2764c41795f..0698b93728b 100644
--- a/Orthtree/include/CGAL/Orthtree_traits_point_3.h
+++ b/Orthtree/include/CGAL/Orthtree_traits_point_3.h
@@ -202,7 +202,7 @@ public:
   template <typename Node_index, typename Tree>
   void distribute_node_contents(Node_index n, Tree& tree, const Point_d& center) {
     CGAL_precondition(!tree.is_leaf(n));
-    reassign_points(n, tree, center, tree.points(n));
+    reassign_points(n, tree, center, tree.data(n));
   }
 
   Point_d get_element(const Node_data_element& index) const {
@@ -224,7 +224,7 @@ private:
 
     // Root case: reached the last dimension
     if (dimension == Dimension::value) {
-      tree.points(tree.child(n, coord.to_ulong())) = points;
+      tree.data(tree.child(n, coord.to_ulong())) = points;
       return;
     }
 
diff --git a/Orthtree/include/CGAL/Orthtree_traits_point_d.h b/Orthtree/include/CGAL/Orthtree_traits_point_d.h
index 23ebb8b7517..243ff8fb29e 100644
--- a/Orthtree/include/CGAL/Orthtree_traits_point_d.h
+++ b/Orthtree/include/CGAL/Orthtree_traits_point_d.h
@@ -176,7 +176,7 @@ public:
   template <typename Node_index, typename Tree>
   void distribute_node_contents(Node_index n, Tree& tree, const Point_d& center) {
     CGAL_precondition(!tree.is_leaf(n));
-    reassign_points(n, tree, center, tree.points(n));
+    reassign_points(n, tree, center, tree.data(n));
   }
 
   Point_d get_element(const Node_data_element& index) const {