diff --git a/AABB_tree/include/CGAL/AABB_tree.h b/AABB_tree/include/CGAL/AABB_tree.h
index 0e6ca291047..8e977c76f57 100644
--- a/AABB_tree/include/CGAL/AABB_tree.h
+++ b/AABB_tree/include/CGAL/AABB_tree.h
@@ -185,7 +185,7 @@ namespace CGAL {
       clear_nodes();
 			m_primitives.clear();
 			clear_search_tree();
-			m_default_search_tree_constructed = m_use_lazy_kd_tree;
+			m_default_search_tree_constructed = true;
 		}
 
 		/// Returns the axis-aligned bounding box of the whole tree.
@@ -440,7 +440,6 @@ public:
 		/// returns `true` iff successful memory allocation
 		bool accelerate_distance_queries() const;
 		///Turns off the lazy construction of the internal search tree.
-		/// Must be called before the first distance query.
 		void do_not_accelerate_distance_queries() const;
 
     /// Constructs an internal KD-tree containing the specified point
@@ -593,7 +592,6 @@ public:
 		// search KD-tree
 		mutable const Search_tree* m_p_search_tree;
 		mutable bool m_search_tree_constructed;
-		mutable bool m_use_lazy_kd_tree;
     mutable bool m_default_search_tree_constructed; // indicates whether the internal kd-tree should be built
     bool m_need_build;
 
@@ -614,7 +612,6 @@ public:
     , m_p_root_node(nullptr)
     , m_p_search_tree(nullptr)
     , m_search_tree_constructed(false)
-    , m_use_lazy_kd_tree(true)
     , m_default_search_tree_constructed(true)
     , m_need_build(false)
   {}
@@ -629,7 +626,6 @@ public:
                 , m_p_root_node(nullptr)
 		, m_p_search_tree(nullptr)
 		, m_search_tree_constructed(false)
-		, m_use_lazy_kd_tree(true)
     , m_default_search_tree_constructed(true)
     , m_need_build(false)
 	{
@@ -760,7 +756,6 @@ public:
 	void AABB_tree<Tr>::do_not_accelerate_distance_queries()const
 	{
 	  clear_search_tree();
-	  m_use_lazy_kd_tree = false;
 	  m_default_search_tree_constructed = false;
 	}
 
diff --git a/Surface_mesh_segmentation/include/CGAL/internal/Surface_mesh_segmentation/SDF_calculation.h b/Surface_mesh_segmentation/include/CGAL/internal/Surface_mesh_segmentation/SDF_calculation.h
index 5c07db3255c..58d85972962 100644
--- a/Surface_mesh_segmentation/include/CGAL/internal/Surface_mesh_segmentation/SDF_calculation.h
+++ b/Surface_mesh_segmentation/include/CGAL/internal/Surface_mesh_segmentation/SDF_calculation.h
@@ -171,9 +171,11 @@ public:
         if(!test)
           tree.insert(Primitive(it, mesh, vertex_point_map));
     }
+    if(!build_kd_tree) {
+      tree.do_not_accelerate_distance_queries();
+    }
     tree.build();
 
-
     if(use_diagonal) {
       CGAL::Bbox_3 bbox = tree.bbox();
       max_diagonal =