diff --git a/Nef_2/include/CGAL/Nef_2/Segment_overlay_traits.h b/Nef_2/include/CGAL/Nef_2/Segment_overlay_traits.h
index 1eecd047efd..639b4781d6e 100644
--- a/Nef_2/include/CGAL/Nef_2/Segment_overlay_traits.h
+++ b/Nef_2/include/CGAL/Nef_2/Segment_overlay_traits.h
@@ -627,6 +627,7 @@ public:
     out << "SweepStatus:\n";
     typename SweepStatus::iterator sit3;
     for( sit3 = YS.begin(); *sit3 != &sh; ++sit3 ) {
+      if (*sit3==&sl) continue;
       int b = orientation(sit3, p_sweep);
       if(*sit3 == &sl) out << " 1";
       else if(*sit3 == &sh) out <<"-1";
diff --git a/Nef_3/include/CGAL/Nef_3/Infimaximal_box.h b/Nef_3/include/CGAL/Nef_3/Infimaximal_box.h
index b1eb8d6b9ee..463b5f85f60 100644
--- a/Nef_3/include/CGAL/Nef_3/Infimaximal_box.h
+++ b/Nef_3/include/CGAL/Nef_3/Infimaximal_box.h
@@ -402,9 +402,9 @@ class Infimaximal_box<Tag_true, Kernel> {
     typename SNC_structure::Vertex_const_iterator v;
     CGAL_forall_vertices(v, snc) {
       Point_3 p(v->point());
-      if(p.hx()[0] > eval) eval = p.hx()[0];
-      if(p.hy()[0] > eval) eval = p.hy()[0];
-      if(p.hz()[0] > eval) eval = p.hz()[0];
+      if(abs(p.hx()[0]) > eval) eval = abs(p.hx()[0]);
+      if(abs(p.hy()[0]) > eval) eval = abs(p.hy()[0]);
+      if(abs(p.hz()[0]) > eval) eval = abs(p.hz()[0]);
     }
     eval *= 4;
     if(eval == 0) return 1;
diff --git a/Nef_3/include/CGAL/Nef_3/K3_tree.h b/Nef_3/include/CGAL/Nef_3/K3_tree.h
index 3bec191d7c2..15392c5d5b9 100644
--- a/Nef_3/include/CGAL/Nef_3/K3_tree.h
+++ b/Nef_3/include/CGAL/Nef_3/K3_tree.h
@@ -517,7 +517,7 @@ Node_handle build_kdtree(Vertex_list& V, Halfedge_list& E, Halffacet_list& F,
 
   int coord = depth%3;
   Point_3 point_on_plane = find_median_point(V, coord);
-  CGAL_NEF_TRACEN("build_kdtree: plane: "<<partition_plane<< " " << point_on_plane);
+//  CGAL_NEF_TRACEN("build_kdtree: plane: "<<partition_plane<< " " << point_on_plane);
 
 #ifdef CGAL_NEF_EXPLOIT_REFERENCE_COUNTING
   Side_of_plane sop(point_on_plane, coord, reference_counted);
diff --git a/Nef_3/include/CGAL/Nef_3/SNC_external_structure.h b/Nef_3/include/CGAL/Nef_3/SNC_external_structure.h
index 336981c8385..3da7dacdaa4 100644
--- a/Nef_3/include/CGAL/Nef_3/SNC_external_structure.h
+++ b/Nef_3/include/CGAL/Nef_3/SNC_external_structure.h
@@ -473,7 +473,7 @@ public:
     CGAL_forall_iterators(it,M4) {
       //    progress++;
       it->second.sort(Halfedge_key_lt());
-      CGAL_NEF_TRACEN("search opposite  "<<it->first);
+      CGAL_NEF_TRACEN("search opposite (M4)  "<<it->first);
       typename Halfedge_list::iterator itl;
       CGAL_forall_iterators(itl,it->second) {
         Halfedge_handle e1 = itl->e;
@@ -482,7 +482,7 @@ public:
         Halfedge_handle e2 = itl->e;
         CGAL_NEF_TRACEN("    " << e1->source()->point()
                         << " -> " << e2->source()->point());
-        CGAL_NEF_TRACEN(e1->vector()<<" -> "<<-e2->vector());
+        CGAL_NEF_TRACEN("    " << e1->vector()<<" -> "<<-e2->vector());
         make_twins(e1,e2);
         CGAL_assertion(e1->mark()==e2->mark());
 
@@ -493,7 +493,7 @@ public:
     CGAL_forall_iterators(it,M3) {
       //    progress++;
       it->second.sort(Halfedge_key_lt());
-      CGAL_NEF_TRACEN("search opposite  "<<it->first);
+      CGAL_NEF_TRACEN("search opposite (M3)  "<<it->first);
       typename Halfedge_list::iterator itl;
       CGAL_forall_iterators(itl,it->second) {
         Halfedge_handle e1 = itl->e;
@@ -502,7 +502,7 @@ public:
         Halfedge_handle e2 = itl->e;
         CGAL_NEF_TRACEN("    " << e1->source()->point()
                         << " -> " << e2->source()->point());
-        CGAL_NEF_TRACEN(e1->vector()<<" -> "<<-e2->vector());
+        CGAL_NEF_TRACEN("    " << e1->vector()<<" -> "<<-e2->vector());
         make_twins(e1,e2);
         CGAL_assertion(e1->mark()==e2->mark());
 
@@ -513,7 +513,7 @@ public:
     CGAL_forall_iterators(it,M2) {
       //    progress++;
       it->second.sort(Halfedge_key_lt());
-      CGAL_NEF_TRACEN("search opposite  "<<it->first);
+      CGAL_NEF_TRACEN("search opposite (M2)  "<<it->first);
       typename Halfedge_list::iterator itl;
       CGAL_forall_iterators(itl,it->second) {
         Halfedge_handle e1 = itl->e;
@@ -522,7 +522,7 @@ public:
         Halfedge_handle e2 = itl->e;
         CGAL_NEF_TRACEN("    " << e1->source()->point()
                         << " -> " << e2->source()->point());
-        CGAL_NEF_TRACEN(e1->vector()<<" -> "<<-e2->vector());
+        CGAL_NEF_TRACEN("    " << e1->vector()<<" -> "<<-e2->vector());
         make_twins(e1,e2);
         CGAL_assertion(e1->mark()==e2->mark());
 
@@ -533,7 +533,7 @@ public:
     CGAL_forall_iterators(it,M) {
       //    progress++;
       it->second.sort(Halfedge_key_lt());
-      CGAL_NEF_TRACEN("search opposite  "<<it->first);
+      CGAL_NEF_TRACEN("search opposite (M)  "<<it->first);
       typename Halfedge_list::iterator itl;
       CGAL_forall_iterators(itl,it->second) {
         Halfedge_handle e1 = itl->e;
@@ -542,7 +542,7 @@ public:
         Halfedge_handle e2 = itl->e;
         CGAL_NEF_TRACEN("    " << e1->source()->point()
                         << " -> " << e2->source()->point());
-        CGAL_NEF_TRACEN(e1->vector()<<" -> "<< -e2->vector());
+        CGAL_NEF_TRACEN("    " << e1->vector()<<" -> "<< -e2->vector());
         CGAL_assertion(e1->source()->point() != e2->source()->point());
         CGAL_assertion(e1->mark()==e2->mark());
         make_twins(e1,e2);
@@ -585,10 +585,16 @@ public:
             break;
       } else
 #endif
+        CGAL_assertion_code(bool found = false;)
         CGAL_For_all(cet,cete)
           if ( cet->circle() == ce->circle().opposite() &&
                cet->source()->twin() == ce->source() )
+        {
+            CGAL_assertion_code(found = true;)
             break;
+        }
+
+        CGAL_assertion(found);
 
 #ifdef CGAL_USE_TRACE
       if( cet->circle() != ce->circle().opposite() )
diff --git a/Nef_3/include/CGAL/Nef_3/SNC_intersection.h b/Nef_3/include/CGAL/Nef_3/SNC_intersection.h
index a3a26fb3041..be8345069e2 100644
--- a/Nef_3/include/CGAL/Nef_3/SNC_intersection.h
+++ b/Nef_3/include/CGAL/Nef_3/SNC_intersection.h
@@ -139,7 +139,7 @@ class SNC_intersection {
     if( !CGAL::assign( p, o))
       return false;
     CGAL_NEF_TRACEN( "-> intersection point: " << p );
-    CGAL_NEF_TRACEN( "-> point in facet interior? "<<point_in_facet_interior( f, p));
+    // CGAL_NEF_TRACEN( "-> point in facet interior? "<<point_in_facet_interior( f, p));
     return point_in_facet_interior( p, f);
   }
 
@@ -159,7 +159,7 @@ class SNC_intersection {
     if( !CGAL::assign( p, o))
       return false;
     CGAL_NEF_TRACEN( "-> intersection point: " << p );
-    CGAL_NEF_TRACEN( "-> point in facet interior? "<<point_in_facet_interior( f, p));
+    // CGAL_NEF_TRACEN( "-> point in facet interior? "<<point_in_facet_interior( f, p));
     return point_in_facet_interior( p, f);
   }
 
diff --git a/Nef_3/include/CGAL/Nef_3/SNC_point_locator.h b/Nef_3/include/CGAL/Nef_3/SNC_point_locator.h
index 9814f10bb6f..13ec1836a2a 100644
--- a/Nef_3/include/CGAL/Nef_3/SNC_point_locator.h
+++ b/Nef_3/include/CGAL/Nef_3/SNC_point_locator.h
@@ -432,7 +432,7 @@ public:
         e = *ei;
         CGAL_NEF_TRACEN("test edge " << e->source()->point() << "->" << e->twin()->source()->point());
         if (SNC_intersection::does_contain_internally(e->source()->point(), e->twin()->source()->point(), p)) {
-          _CGAL_NEF_TRACEN("found on edge "<< ss);
+//          _CGAL_NEF_TRACEN("found on edge "<< ss);
           return make_object(e);
         }
         if((e->source() != v)  && (e->twin()->source() != v) &&
@@ -557,7 +557,7 @@ private:
           if(SNC_intersection::does_intersect_internally( s, *f, q) ) {
             q = normalized(q);
             call_back( e0, *f, q);
-            _CGAL_NEF_TRACEN("edge intersects facet on plane "<<f->plane()<<" on "<<q);
+//            _CGAL_NEF_TRACEN("edge intersects facet on plane "<<f->plane()<<" on "<<q);
           }
           visited[*f] = true;
         }
diff --git a/Nef_3/test/Nef_3/issue8644bis.cpp b/Nef_3/test/Nef_3/issue8644bis.cpp
new file mode 100644
index 00000000000..1424419e6cf
--- /dev/null
+++ b/Nef_3/test/Nef_3/issue8644bis.cpp
@@ -0,0 +1,18 @@
+#include <CGAL/Extended_cartesian.h>
+#include <CGAL/Exact_rational.h>
+#include <CGAL/Nef_polyhedron_3.h>
+
+using Kernel = CGAL::Extended_cartesian<CGAL::Exact_rational>;
+using Nef = CGAL::Nef_polyhedron_3<Kernel>;
+
+int main()
+{
+  Nef hspace_1(Nef::Plane_3(1.0, 0.0, 0.0, 0.0), Nef::INCLUDED);
+  Nef hspace_2(Nef::Plane_3(1.0, 0.0, 0.0, 1.0), Nef::INCLUDED);
+  Nef hspace_3(Nef::Plane_3(0.0, 0.0, 1.0, 1.0), Nef::INCLUDED);
+
+  Nef intersection_1 = hspace_1*hspace_2;
+  Nef intersection_2 = hspace_2*hspace_3;
+
+  return 0;
+}