diff --git a/Nef_3/examples/Nef_3/nef_3_simple.cpp b/Nef_3/examples/Nef_3/nef_3_simple.cpp
index 4906af16f31..5902ad85b20 100644
--- a/Nef_3/examples/Nef_3/nef_3_simple.cpp
+++ b/Nef_3/examples/Nef_3/nef_3_simple.cpp
@@ -10,5 +10,6 @@ int main() {
   Nef_polyhedron N1(Nef_polyhedron::COMPLETE);
 
   CGAL_assertion (N0 == N1.complement());
+  CGAL_assertion (N0 != N1);
   return 0;
 }
diff --git a/Nef_3/include/CGAL/Nef_polyhedron_3.h b/Nef_3/include/CGAL/Nef_polyhedron_3.h
index 9f3c59bfae1..fa45cb647d4 100644
--- a/Nef_3/include/CGAL/Nef_polyhedron_3.h
+++ b/Nef_3/include/CGAL/Nef_polyhedron_3.h
@@ -1372,6 +1372,10 @@ protected:
   intersection(const Nef_polyhedron_3<Kernel,Items, Mark>& N1) const
     /*{\Mop returns |\Mvar| $\cap$ |N1|. }*/ {
     CGAL_NEF_TRACEN(" intersection between nef3 "<<&*this<<" and "<<&N1);
+    if (is_empty()) return *this;
+    if (N1.is_empty()) return N1;
+    if (is_space()) return N1;
+    if (N1.is_space()) return *this;
     AND _and;
     SNC_structure rsnc;
     Nef_polyhedron_3<Kernel,Items, Mark> res(rsnc, new SNC_point_locator_default, false);
@@ -1396,6 +1400,10 @@ protected:
   join(const Nef_polyhedron_3<Kernel,Items, Mark>& N1) const
   /*{\Mop returns |\Mvar| $\cup$ |N1|. }*/ { 
     CGAL_NEF_TRACEN(" join between nef3 "<<&*this<<" and "<<&N1);
+    if (is_empty()) return N1;
+    if (N1.is_empty()) return *this;
+    if (is_space()) return *this;
+    if (N1.is_space()) return N1;
     OR _or;
     //CGAL::binop_intersection_tests_allpairs<SNC_decorator, OR> tests_impl;
     SNC_structure rsnc;
@@ -1409,6 +1417,10 @@ protected:
   difference(const Nef_polyhedron_3<Kernel,Items, Mark>& N1) const
   /*{\Mop returns |\Mvar| $-$ |N1|. }*/ { 
     CGAL_NEF_TRACEN(" difference between nef3 "<<&*this<<" and "<<&N1);
+    if (is_empty()) return *this;
+    if (N1.is_empty()) return *this;
+    if (is_space()) return N1.complement();
+    if (N1.is_space()) return Nef_polyhedron_3(EMPTY);
     DIFF _diff;
     //CGAL::binop_intersection_tests_allpairs<SNC_decorator, DIFF> tests_impl;
     SNC_structure rsnc;
@@ -1423,6 +1435,10 @@ protected:
   /*{\Mop returns the symmectric difference |\Mvar - T| $\cup$ 
           |T - \Mvar|. }*/ {
     CGAL_NEF_TRACEN(" symmetic difference between nef3 "<<&*this<<" and "<<&N1);
+    if (is_empty()) return N1;
+    if (N1.is_empty()) return *this;
+    if (is_space()) return Nef_polyhedron_3(EMPTY);
+    if (N1.is_space()) return Nef_polyhedron_3(EMPTY);
     XOR _xor;
     //CGAL::binop_intersection_tests_allpairs<SNC_decorator, XOR> tests_impl;
     SNC_structure rsnc;