diff --git a/Spatial_searching/include/CGAL/Kd_tree.h b/Spatial_searching/include/CGAL/Kd_tree.h
index 350b9f533d8..2d47eab2d12 100644
--- a/Spatial_searching/include/CGAL/Kd_tree.h
+++ b/Spatial_searching/include/CGAL/Kd_tree.h
@@ -196,7 +196,7 @@ class Kd_tree {
     if (try_parallel_internal_node_creation (nh, c, c_low, tag))
       return;
 
-    if (c_low.size() > split.bucket_size())
+    if (c_low.size() > split.bucket_size() && c_low.max_tight_spread() > 0)
     {
       nh->lower_ch = new_internal_node();
       create_internal_node (nh->lower_ch, c_low, tag);
@@ -204,7 +204,7 @@ class Kd_tree {
     else
       nh->lower_ch = create_leaf_node(c_low);
 
-    if (c.size() > split.bucket_size())
+    if (c.size() > split.bucket_size() && c.max_tight_spread() > 0)
     {
       nh->upper_ch = new_internal_node();
       create_internal_node (nh->upper_ch, c, tag);
@@ -341,7 +341,7 @@ class Kd_tree {
 
     Point_container c(dim_, data.begin(), data.end(),traits_);
     bbox = new Kd_tree_rectangle<FT,D>(c.bounding_box());
-    if (c.size() <= split.bucket_size()){
+    if (c.size() <= split.bucket_size() || c.max_tight_spread() == 0){
       tree_root = create_leaf_node(c);
     }else {
        tree_root = new_internal_node();