diff --git a/src/detail/GeometrySet.cpp b/src/detail/GeometrySet.cpp
old mode 100644
new mode 100755
index 078e7862..ffa0a76c
--- a/src/detail/GeometrySet.cpp
+++ b/src/detail/GeometrySet.cpp
@@ -558,10 +558,10 @@ void recompose_points( const typename GeometrySet<Dim>::PointCollection& points,
 // compare less than
 struct ComparePoints {
     bool operator()( const CGAL::Point_2<Kernel>& lhs, const CGAL::Point_2<Kernel>& rhs ) const {
-        return lhs.x() == rhs.x() ? lhs.y() < rhs.y() : lhs.x() < rhs.x();
+        return lhs.x() < rhs.x() || lhs.y() < rhs.y();
     }
     bool operator()( const CGAL::Point_3<Kernel>& lhs, const CGAL::Point_3<Kernel>& rhs ) const {
-        return lhs.x() == rhs.x() ? (lhs.y() == rhs.y() ? lhs.z() < rhs.z() : lhs.y() < rhs.y()) : lhs.x() < rhs.x();
+        return lhs.x() < rhs.x() || lhs.y() < rhs.y() || lhs.z() < rhs.z();
     }
 };
 
@@ -922,37 +922,78 @@ void GeometrySet<Dim>::collectPoints( const PrimitiveHandle<Dim>& pa )
 }
 
 template <int Dim, class IT>
-void _filter_covered( IT ibegin, IT iend, GeometrySet<Dim>& output )
+void _filter_covered(IT ibegin, IT iend, GeometrySet<Dim>& output)
 {
-    for ( IT it = ibegin; it != iend; ++it ) {
-        GeometrySet<Dim> v1;
-        v1.addPrimitive( it->primitive() );
-        bool v1_covered = false;
-
-        for ( IT it2 = it; it2 != iend; ++it2 ) {
-            if ( it == it2 ) {
-                continue;
+   for (IT it = ibegin; it != iend; ++it)
+   {
+      GeometrySet<Dim> v1;
+      v1.addPrimitive(it->primitive());
+      std::auto_ptr<SFCGAL::Geometry> g1 = v1.recompose();
+
+      bool v1_covered = false;
+      for (IT it2 = it; it2 != iend; ++it2)
+      {
+         if (it == it2)
+         {
+            continue;
+         }
+
+         GeometrySet<Dim> v2;
+         v2.addPrimitive(it2->primitive());
+
+         bool b = false;
+         if (g1->is3D())
+         {
+            std::auto_ptr<SFCGAL::Geometry> g2 = v2.recompose();
+            if (g2->is3D())
+            {
+               b = algorithm::covers3D(*g2,*g1);
             }
-
-            GeometrySet<Dim> v2;
-            v2.addPrimitive( it2->primitive() );
-
-            if ( algorithm::covers( v2, v1 ) ) {
-                v1_covered = true;
-                break;
+            else
+            {
+               b = algorithm::covers(v2,v1);
             }
-        }
-
-        // if its not covered by another primitive
-        if ( !v1_covered ) {
-            // and not covered by another already inserted primitive
-            bool b = algorithm::covers( output, v1 );
-
-            if ( !b ) {
-                output.addPrimitive( it->primitive(), it->flags() );
+         }
+         else
+         {
+            b = algorithm::covers(v2,v1);
+         }
+
+         if (b)
+         {
+            v1_covered = true;
+            break;
+         }
+      }
+
+      // If its not covered by another primitive...
+      if (!v1_covered)
+      {
+         // ...and not covered by another already inserted primitive...
+         bool b;
+         if (g1->is3D())
+         {
+            std::auto_ptr<SFCGAL::Geometry> goutput = output.recompose();
+            if (goutput->is3D())
+            {
+               b = algorithm::covers3D(*goutput,*g1);
             }
-        }
-    }
+            else
+            {
+               b = algorithm::covers(output,v1);
+            }
+         }
+         else
+         {
+            b = algorithm::covers(output,v1);
+         }
+
+         if (!b)
+         {
+            output.addPrimitive(it->primitive(), it->flags());
+         }
+      }
+   }
 }
 
 template <>