diff --git a/Box_intersection_d/include/CGAL/Box_intersection_d/segment_tree.h b/Box_intersection_d/include/CGAL/Box_intersection_d/segment_tree.h
index e6a9ca0e05e..5c31223d85a 100644
--- a/Box_intersection_d/include/CGAL/Box_intersection_d/segment_tree.h
+++ b/Box_intersection_d/include/CGAL/Box_intersection_d/segment_tree.h
@@ -345,10 +345,37 @@ void segment_tree( RandomAccessIter1 p_begin, RandomAccessIter1 p_end,
     const T inf = box_limits< T >::inf();
     const T sup = box_limits< T >::sup();
 
+#if CGAL_BOX_INTERSECTION_DEBUG
+  CGAL_STATIC_THREAD_LOCAL_VARIABLE(int, level, -1);
+    Counter<int> bla( level );
+    CGAL_BOX_INTERSECTION_DUMP("range: [" << lo << "," << hi << ") dim " 
+                                          << dim << std::endl )
+    CGAL_BOX_INTERSECTION_DUMP("intervals: " )
+    //dump_box_numbers( i_begin, i_end, traits );
+    dump_intervals( i_begin, i_end, traits, dim );
+    CGAL_BOX_INTERSECTION_DUMP("points: " )
+    //dump_box_numbers( p_begin, p_end, traits );
+    dump_points( p_begin, p_end, traits, dim );
+#endif
+
+#if CGAL_SEGMENT_TREE_CHECK_INVARIANTS
+    {
+        // first: each point is inside segment [lo,hi)
+        for( RandomAccessIter1 it = p_begin; it != p_end; ++it ) {
+            CGAL_assertion( Lo_less( hi, dim )(*it) );
+            CGAL_assertion( Lo_less( lo, dim )(*it) == false );
+        }
+        // second: each interval intersects segment [lo,hi)
+        for( RandomAccessIter2 it = i_begin; it != i_end; ++it )
+            CGAL_assertion( Hi_greater(lo,dim)(*it) && Lo_less(hi,dim)(*it));
+    }
+#endif
+
     if( p_begin == p_end || i_begin == i_end || lo >= hi )
         return;
 
     if( dim == 0 )  {
+        CGAL_BOX_INTERSECTION_DUMP( "dim = 0. scanning ... " << std::endl )
         one_way_scan( p_begin, p_end, i_begin, i_end,
                       callback, traits, dim, in_order );
         return;
@@ -357,6 +384,7 @@ void segment_tree( RandomAccessIter1 p_begin, RandomAccessIter1 p_end,
     if( std::distance( p_begin, p_end ) < cutoff ||
         std::distance( i_begin, i_end ) < cutoff  )
     {
+        CGAL_BOX_INTERSECTION_DUMP( "scanning ... " << std::endl )
         modified_two_way_scan( p_begin, p_end, i_begin, i_end,
                                callback, traits, dim, in_order );
         return;
@@ -366,7 +394,8 @@ void segment_tree( RandomAccessIter1 p_begin, RandomAccessIter1 p_end,
         std::partition( i_begin, i_end, Spanning( lo, hi, dim ) );
 
     if( i_begin != i_span_end ) {
-
+        CGAL_BOX_INTERSECTION_DUMP( "checking spanning intervals ... " 
+                                    << std::endl )
         // make two calls for roots of segment tree at next level.
         segment_tree( p_begin, p_end, i_begin, i_span_end, inf, sup,
                       callback, traits, cutoff, dim - 1,  in_order );
@@ -378,6 +407,10 @@ void segment_tree( RandomAccessIter1 p_begin, RandomAccessIter1 p_end,
     RandomAccessIter1 p_mid = split_points( p_begin, p_end, traits, dim, mi );
 
     if( p_mid == p_begin || p_mid == p_end )  {
+        CGAL_BOX_INTERSECTION_DUMP( "unable to split points! ")
+        //dump_points( p_begin, p_end, traits, dim );
+        CGAL_BOX_INTERSECTION_DUMP( "performing modified two_way_san ... " 
+                                     << std::endl )
         modified_two_way_scan( p_begin, p_end, i_span_end, i_end,
                                callback, traits, dim, in_order );
         return;
@@ -387,17 +420,21 @@ void segment_tree( RandomAccessIter1 p_begin, RandomAccessIter1 p_end,
     // separate left intervals.
     // left intervals have a low point strictly less than mi
     i_mid = std::partition( i_span_end, i_end, Lo_less( mi, dim ) );
-
+    CGAL_BOX_INTERSECTION_DUMP("->left" << std::endl )
     segment_tree( p_begin, p_mid, i_span_end, i_mid, lo, mi,
                   callback, traits, cutoff, dim, in_order );
     // separate right intervals.
     // right intervals have a high point strictly higher than mi
     i_mid = std::partition( i_span_end, i_end, Hi_greater( mi, dim ) );
-
+    CGAL_BOX_INTERSECTION_DUMP("->right"<< std::endl )
     segment_tree( p_mid, p_end, i_span_end, i_mid, mi, hi,
                   callback, traits, cutoff, dim, in_order );
 }
 
+#if CGAL_BOX_INTERSECTION_DEBUG
+ #undef CGAL_BOX_INTERSECTION_DUMP
+#endif
+#undef CGAL_BOX_INTERSECTION_DEBUG
 
 } // end namespace Box_intersection_d