diff --git a/Nef_3/include/CGAL/Nef_3/Mark_bounded_volumes.h b/Nef_3/include/CGAL/Nef_3/Mark_bounded_volumes.h
index f5af77cf1d5..0ce560af241 100644
--- a/Nef_3/include/CGAL/Nef_3/Mark_bounded_volumes.h
+++ b/Nef_3/include/CGAL/Nef_3/Mark_bounded_volumes.h
@@ -15,8 +15,8 @@
 
 #include <CGAL/license/Nef_3.h>
 
-
-#include <CGAL/Nef_polyhedron_3.h>
+#include <CGAL/Modifier_base.h>
+#include <CGAL/Nef_3/SNC_iteration.h>
 
 namespace CGAL {
 
diff --git a/Nef_3/include/CGAL/Nef_3/SNC_constructor.h b/Nef_3/include/CGAL/Nef_3/SNC_constructor.h
index c79d68de6d5..bbd9d5b1d41 100644
--- a/Nef_3/include/CGAL/Nef_3/SNC_constructor.h
+++ b/Nef_3/include/CGAL/Nef_3/SNC_constructor.h
@@ -24,12 +24,11 @@
 #include <CGAL/Nef_S2/Normalizing.h>
 #include <CGAL/Nef_3/bounded_side_3.h>
 #include <CGAL/Nef_3/Pluecker_line_3.h>
-#include <CGAL/Nef_3/SNC_decorator.h>
 #include <CGAL/Nef_3/SNC_SM_overlayer.h>
 #include <CGAL/Nef_S2/SM_point_locator.h>
+#include <CGAL/Nef_3/SNC_halfedge_key.h>
 #include <CGAL/Nef_3/SNC_sphere_map.h>
 #include <CGAL/Nef_3/SNC_intersection.h>
-#include <CGAL/Nef_3/SNC_external_structure.h>
 #ifdef SM_VISUALIZOR
 #include <CGAL/Nef_3/SNC_SM_visualizor.h>
 #endif // SM_VISUALIZOR
@@ -41,6 +40,9 @@
 
 namespace CGAL {
 
+template <typename T>
+class SNC_io_parser;
+
 template <typename Infi_box, typename Vertex_handle>
 struct Frame_point_lt {
 
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 038843e9fa1..336981c8385 100644
--- a/Nef_3/include/CGAL/Nef_3/SNC_external_structure.h
+++ b/Nef_3/include/CGAL/Nef_3/SNC_external_structure.h
@@ -25,7 +25,7 @@
 #include <CGAL/Nef_3/SNC_point_locator.h>
 #include <CGAL/Nef_S2/SM_point_locator.h>
 #include <CGAL/Nef_3/SNC_FM_decorator.h>
-#include <CGAL/Nef_3/SNC_io_parser.h>
+#include <CGAL/Nef_3/SNC_halfedge_key.h>
 #include <CGAL/Nef_3/SNC_indexed_items.h>
 #include <CGAL/Nef_3/SNC_simplify.h>
 #include <map>
@@ -40,77 +40,6 @@
 
 namespace CGAL {
 
-struct int_lt {
-  bool operator()(const int& i1, const int& i2) const { return i1<i2; }
-};
-template <typename Edge_handle>
-struct Halfedge_key_lt4 {
-
-  bool operator()(const Edge_handle& e1, const Edge_handle& e2) const {
-    if(CGAL::sign(e1->point().x()) != 0) {
-      if(e1->source() != e2->source())
-        return CGAL::compare_x(e1->source()->point(), e2->source()->point()) < 0;
-      else
-        return e1->point().x() < 0;
-    }
-    if(CGAL::sign(e1->point().y()) != 0) {
-      if(e1->source() != e2->source())
-        return CGAL::compare_y(e1->source()->point(), e2->source()->point()) < 0;
-      else
-        return e1->point().y() < 0;
-    }
-    if(e1->source() != e2->source())
-      return CGAL::compare_z(e1->source()->point(), e2->source()->point()) < 0;
-    return e1->point().z() < 0;
-  }
-};
-
-template <typename Edge_handle>
-struct Halfedge_key_lt3 {
-
-  bool operator()(const Edge_handle& e1, const Edge_handle& e2) const {
-    if(e1->source() != e2->source())
-      return CGAL::lexicographically_xyz_smaller(e1->source()->point(), e2->source()->point());
-    if(CGAL::sign(e1->point().x()) != 0)
-      return e1->point().x() < 0;
-    if(CGAL::sign(e1->point().y()) != 0)
-      return e1->point().y() < 0;
-    return e1->point().z() < 0;
-  }
-};
-
-template <typename Point, typename Edge>
-struct Halfedge_key {
-  typedef Halfedge_key<Point,Edge> Self;
-  Point p; int i; Edge e;
-  Halfedge_key(Point pi, int ii, Edge ei) :
-    p(pi), i(ii), e(ei) {}
-  Halfedge_key(const Self& k) : p(k.p), i(k.i), e(k.e) {}
-  Self& operator=(const Self& k) { p=k.p; i=k.i; e=k.e; return *this; }
-  bool operator==(const Self& k) const { return p==k.p && i==k.i; }
-  bool operator!=(const Self& k) const { return !operator==(k); }
-};
-
-template <typename Point, typename Edge, class Decorator>
-struct Halfedge_key_lt {
-  typedef Halfedge_key<Point,Edge> Key;
-  typedef typename Point::R R;
-  typedef typename R::Vector_3 Vector;
-  typedef typename R::Direction_3 Direction;
-  bool operator()( const Key& k1, const Key& k2) const {
-    if( k1.e->source() == k2.e->source())
-      return (k1.i < k2.i);
-    Direction l(k1.e->vector());
-    if( k1.i < 0) l = -l;
-    return (Direction( k2.p - k1.p) == l);
-  }
-};
-
-template <typename Point, typename Edge>
-std::ostream& operator<<(std::ostream& os,
-                         const Halfedge_key<Point,Edge>& k )
-{ os << k.p << " " << k.i; return os; }
-
 template <typename R>
 int sign_of(const CGAL::Plane_3<R>& h)
 { if ( h.c() != 0 ) return CGAL_NTS sign(h.c());
diff --git a/Nef_3/include/CGAL/Nef_3/SNC_halfedge_key.h b/Nef_3/include/CGAL/Nef_3/SNC_halfedge_key.h
new file mode 100644
index 00000000000..4c2738e63f8
--- /dev/null
+++ b/Nef_3/include/CGAL/Nef_3/SNC_halfedge_key.h
@@ -0,0 +1,95 @@
+// Copyright (c) 1997-2002  Max-Planck-Institute Saarbruecken (Germany).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+//
+// Author(s)     : Peter Hachenberger <hachenberger@mpi-sb.mpg.de>
+
+#ifndef CGAL_SNC_HALFEDGE_KEY_H
+#define CGAL_SNC_HALFEDGE_KEY_H
+
+#include <CGAL/license/Nef_3.h>
+
+#include <CGAL/Kernel/global_functions.h>
+
+namespace CGAL {
+
+struct int_lt {
+  bool operator()(const int& i1, const int& i2) const { return i1<i2; }
+};
+
+template <typename Edge_handle>
+struct Halfedge_key_lt4 {
+
+  bool operator()(const Edge_handle& e1, const Edge_handle& e2) const {
+    if(CGAL::sign(e1->point().x()) != 0) {
+      if(e1->source() != e2->source())
+        return CGAL::compare_x(e1->source()->point(), e2->source()->point()) < 0;
+      else
+        return e1->point().x() < 0;
+    }
+    if(CGAL::sign(e1->point().y()) != 0) {
+      if(e1->source() != e2->source())
+        return CGAL::compare_y(e1->source()->point(), e2->source()->point()) < 0;
+      else
+        return e1->point().y() < 0;
+    }
+    if(e1->source() != e2->source())
+      return CGAL::compare_z(e1->source()->point(), e2->source()->point()) < 0;
+    return e1->point().z() < 0;
+  }
+};
+
+template <typename Edge_handle>
+struct Halfedge_key_lt3 {
+
+  bool operator()(const Edge_handle& e1, const Edge_handle& e2) const {
+    if(e1->source() != e2->source())
+      return CGAL::lexicographically_xyz_smaller(e1->source()->point(), e2->source()->point());
+    if(CGAL::sign(e1->point().x()) != 0)
+      return e1->point().x() < 0;
+    if(CGAL::sign(e1->point().y()) != 0)
+      return e1->point().y() < 0;
+    return e1->point().z() < 0;
+  }
+};
+
+template <typename Point, typename Edge>
+struct Halfedge_key {
+  typedef Halfedge_key<Point,Edge> Self;
+  Point p; int i; Edge e;
+  Halfedge_key(Point pi, int ii, Edge ei) :
+    p(pi), i(ii), e(ei) {}
+  Halfedge_key(const Self& k) : p(k.p), i(k.i), e(k.e) {}
+  Self& operator=(const Self& k) { p=k.p; i=k.i; e=k.e; return *this; }
+  bool operator==(const Self& k) const { return p==k.p && i==k.i; }
+  bool operator!=(const Self& k) const { return !operator==(k); }
+};
+
+template <typename Point, typename Edge, class Decorator>
+struct Halfedge_key_lt {
+  typedef Halfedge_key<Point,Edge> Key;
+  typedef typename Point::R R;
+  typedef typename R::Vector_3 Vector;
+  typedef typename R::Direction_3 Direction;
+  bool operator()( const Key& k1, const Key& k2) const {
+    if( k1.e->source() == k2.e->source())
+      return (k1.i < k2.i);
+    Direction l(k1.e->vector());
+    if( k1.i < 0) l = -l;
+    return (Direction( k2.p - k1.p) == l);
+  }
+};
+
+template <typename Point, typename Edge>
+std::ostream& operator<<(std::ostream& os,
+                         const Halfedge_key<Point,Edge>& k )
+{ os << k.p << " " << k.i; return os; }
+
+}
+#endif //CGAL_SNC_HALFEDGE_KEY_H
diff --git a/Nef_3/include/CGAL/Nef_3/SNC_io_parser.h b/Nef_3/include/CGAL/Nef_3/SNC_io_parser.h
index aab28de6795..9aa445f38a1 100644
--- a/Nef_3/include/CGAL/Nef_3/SNC_io_parser.h
+++ b/Nef_3/include/CGAL/Nef_3/SNC_io_parser.h
@@ -24,7 +24,6 @@
 #include <CGAL/Nef_S2/SM_decorator.h>
 #include <CGAL/Nef_3/SNC_structure.h>
 #include <CGAL/Nef_3/SNC_decorator.h>
-#include <CGAL/Nef_3/SNC_constructor.h>
 #include <CGAL/Nef_2/Object_index.h>
 #include <CGAL/Nef_S2/Normalizing.h>
 #include <vector>
diff --git a/Nef_3/include/CGAL/Nef_3/vertex_cycle_to_nef_3.h b/Nef_3/include/CGAL/Nef_3/vertex_cycle_to_nef_3.h
index 1b7426fee5a..750fcf86ffe 100644
--- a/Nef_3/include/CGAL/Nef_3/vertex_cycle_to_nef_3.h
+++ b/Nef_3/include/CGAL/Nef_3/vertex_cycle_to_nef_3.h
@@ -28,10 +28,7 @@
 #include <CGAL/Constrained_triangulation_plus_2.h>
 
 // Nef polyhedra
-#include <CGAL/Nef_polyhedron_3.h>
-#include <CGAL/Nef_3/SNC_structure.h>
-#include <CGAL/Nef_3/SNC_constructor.h>
-#include <CGAL/Nef_3/SNC_point_locator.h>
+#include <CGAL/Nef_3/SNC_indexed_items.h>
 
 namespace CGAL {