diff --git a/Spatial_searching/include/CGAL/Orthogonal_incremental_neighbor_search.h b/Spatial_searching/include/CGAL/Orthogonal_incremental_neighbor_search.h
index 932265f82ce..13eca80ece1 100644
--- a/Spatial_searching/include/CGAL/Orthogonal_incremental_neighbor_search.h
+++ b/Spatial_searching/include/CGAL/Orthogonal_incremental_neighbor_search.h
@@ -174,7 +174,7 @@ namespace CGAL {
          else{
            distance_to_root=
    	 Orthogonal_distance_instance.max_distance_to_rectangle(q,
-						tree.bounding_box());
+						tree.bounding_box(), dists);
            Node_with_distance *The_Root = new Node_with_distance(tree.root(),
                                                                  distance_to_root, dists);
         PriorityQueue.push(The_Root);
@@ -372,10 +372,9 @@ namespace CGAL {
             FT diff1 = val - node->upper_low_value();
             FT diff2 = val - node->lower_high_value();
 	    if (diff1 + diff2 < FT(0.0)) {
+              diff1 = val - node->upper_high_value();
               new_rd=
 		Orthogonal_distance_instance.new_distance(copy_rd,dst,diff1,new_cut_dim);
-                
-	      CGAL_assertion(new_rd >= copy_rd);
 		Node_with_distance *Lower_Child =
 		  new Node_with_distance(node->lower(), copy_rd, dists);
 		PriorityQueue.push(Lower_Child);
@@ -385,8 +384,8 @@ namespace CGAL {
 
 	    }
 	    else { // compute new distance
+              diff2 = val - node->lower_low_value();
 	      new_rd=Orthogonal_distance_instance.new_distance(copy_rd,dst,diff2,new_cut_dim);  
-	      CGAL_assertion(new_rd >= copy_rd);
 		Node_with_distance *Upper_Child =
 		  new Node_with_distance(node->upper(), copy_rd, dists);
 		PriorityQueue.push(Upper_Child);