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 1eecd047efd7..639b4781d6e3 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 @@ class stl_seg_overlay_traits {
     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/K3_tree.h b/Nef_3/include/CGAL/Nef_3/K3_tree.h
index 3bec191d7c23..15392c5d5b96 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 336981c83850..f2e0683611a6 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 @@ class SNC_external_structure_base : public SNC_decorator<SNC_structure_>
     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 @@ class SNC_external_structure_base : public SNC_decorator<SNC_structure_>
         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 @@ class SNC_external_structure_base : public SNC_decorator<SNC_structure_>
     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 @@ class SNC_external_structure_base : public SNC_decorator<SNC_structure_>
         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 @@ class SNC_external_structure_base : public SNC_decorator<SNC_structure_>
     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 @@ class SNC_external_structure_base : public SNC_decorator<SNC_structure_>
         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 @@ class SNC_external_structure_base : public SNC_decorator<SNC_structure_>
     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 @@ class SNC_external_structure_base : public SNC_decorator<SNC_structure_>
         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 @@ class SNC_external_structure_base : public SNC_decorator<SNC_structure_>
             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() )
+        {
+            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 a3a26fb30415..be8345069e2f 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 9814f10bb6f8..13ec1836a2ad 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 @@ class SNC_point_locator_by_spatial_subdivision :
         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 @@ class SNC_point_locator_by_spatial_subdivision :
           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/issue8644.cpp b/Nef_3/test/Nef_3/issue8644.cpp
index 40b3ac15f473..3180b638fcfb 100644
--- a/Nef_3/test/Nef_3/issue8644.cpp
+++ b/Nef_3/test/Nef_3/issue8644.cpp
@@ -1,5 +1,3 @@
-
-
 #include <CGAL/Extended_cartesian.h>
 #include <CGAL/Exact_rational.h>
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
@@ -8,12 +6,10 @@
 #include <CGAL/Polygon_mesh_processing/orientation.h>
 #include <CGAL/Nef_polyhedron_3.h>
 
-#define DATA_DIR  std::string("./data/")+
+using AFT=CGAL::Exact_rational;
+using AExtended_kernel=CGAL::Extended_cartesian<AFT>;
+using ANef_polyhedron_3=CGAL::Nef_polyhedron_3<AExtended_kernel>;
 
-///////////////////////////////////////////////////////////////////////////////
-using AFT=CGAL::Exact_rational; //CGAL::Gmpzf; CGAL::Exact_rational CGAL::Exact_integer
-using AExtended_kernel=CGAL::Extended_cartesian<AFT>; //CGAL::Exact_predicates_exact_constructions_kernel ; //CGAL::Filtered_extended_homogeneous<RT>;
-using ANef_polyhedron_3=CGAL::Nef_polyhedron_3<AExtended_kernel>;//CGAL::Exact_predicates_exact_constructions_kernel>;
 template<typename SM>
 void compute_volume_kernel_surface_mesh(SM& sm,
                                         ANef_polyhedron_3& res)
@@ -30,7 +26,7 @@ void compute_volume_kernel_surface_mesh(SM& sm,
     res*=ANef_polyhedron_3(eplane);
   }
 }
-////////////////////////////////////////////////////////////////////////////////
+
 void test_sm(const std::string& filename, bool rev)
 {
   CGAL::Surface_mesh<CGAL::Exact_predicates_inexact_constructions_kernel::Point_3> sm;
@@ -45,18 +41,17 @@ void test_sm(const std::string& filename, bool rev)
   compute_volume_kernel_surface_mesh(sm, res);
 
   if(res.is_empty())
-  { std::cout<<"["<<filename<<"]: empty kernel."<<std::endl;}
+    std::cout<<"["<<filename<<"]: empty kernel."<<std::endl;
   else
-  { std::cout<<"["<<filename<<"]: NON empty kernel."<<std::endl;}
+    std::cout<<"["<<filename<<"]: NON empty kernel."<<std::endl;
 }
-////////////////////////////////////////////////////////////////////////////////
-////////////////////////////////////////////////////////////////////////////////
+
 int main(/* int argc, char** argv */)
 {
-  test_sm(std::string(DATA_DIR"lshape1_dim3.off"), true);
-  test_sm(std::string(DATA_DIR"lshape1_dim3.off"), false);
-  test_sm(std::string(DATA_DIR"ushape1_dim3.off"), true);
-  test_sm(std::string(DATA_DIR"ushape1_dim3.off"), false);
+  test_sm(std::string("data/lshape1_dim3.off"), true);
+  test_sm(std::string("data/lshape1_dim3.off"), false);
+  test_sm(std::string("data/ushape1_dim3.off"), true);
+  test_sm(std::string("data/ushape1_dim3.off"), false);
   return 0;
 }
 
diff --git a/Nef_3/test/Nef_3/issue8644bis.cpp b/Nef_3/test/Nef_3/issue8644bis.cpp
index f419094bfc6d..6968f704c4e9 100644
--- a/Nef_3/test/Nef_3/issue8644bis.cpp
+++ b/Nef_3/test/Nef_3/issue8644bis.cpp
@@ -5,14 +5,14 @@
 using Kernel = CGAL::Extended_cartesian<CGAL::Gmpq>;
 using Nef = CGAL::Nef_polyhedron_3<Kernel>;
 
-int main(int argc, char ** argv)
+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; // Line 14. Works fine.
-  Nef intersection_2 = hspace_2*hspace_3; // Line 15. Assertion failure.
-  
+  Nef intersection_1 = hspace_1*hspace_2;
+  Nef intersection_2 = hspace_2*hspace_3;
+
   return 0;
 }