diff --git a/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_garland_heckbert.cpp b/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_garland_heckbert.cpp
index 7d2f9500b5d..6b2b21bd401 100644
--- a/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_garland_heckbert.cpp
+++ b/Surface_mesh_simplification/examples/Surface_mesh_simplification/edge_collapse_garland_heckbert.cpp
@@ -24,6 +24,7 @@ typedef SMS::GarlandHeckbert_plane_policies<Surface_mesh, Kernel>
 typedef SMS::GarlandHeckbert_probabilistic_plane_policies<Surface_mesh, Kernel>    Prob_plane;
 typedef SMS::GarlandHeckbert_triangle_policies<Surface_mesh, Kernel>               Classic_tri;
 typedef SMS::GarlandHeckbert_probabilistic_triangle_policies<Surface_mesh, Kernel> Prob_tri;
+typedef SMS::GarlandHeckbert_plane_plus_line_policies<Surface_mesh, Kernel>        Plane_plus_line;
 
 template <typename GHPolicies>
 void collapse_gh(Surface_mesh& mesh,
@@ -59,7 +60,7 @@ void collapse_gh(Surface_mesh& mesh,
 
 // Usage:
 // ./command [input] [ratio] [policy] [output]
-// policy can be "cp" (classic plane), "ct" (classic triangle), "pp" (probabilistic plane), "pt" (probabilistic triangle)
+// policy can be "cp" (classic plane), "ct" (classic triangle), "pp" (probabilistic plane), "pt" (probabilistic triangle), "pl" (plane plus line)
 int main(int argc, char** argv)
 {
   Surface_mesh mesh;
@@ -91,8 +92,10 @@ int main(int argc, char** argv)
     collapse_gh<Classic_tri>(mesh, ratio);
   else if(policy == "pp")
     collapse_gh<Prob_plane>(mesh, ratio);
-  else
+  else if(policy == "pt")
     collapse_gh<Prob_tri>(mesh, ratio);
+  else
+    collapse_gh<Plane_plus_line>(mesh, ratio);
 
   CGAL::IO::write_polygon_mesh((argc > 4) ? argv[4] : "out.off", mesh, CGAL::parameters::stream_precision(17));
 
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_plane_plus_line_policies.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_plane_plus_line_policies.h
new file mode 100644
index 00000000000..b5fc0dad24f
--- /dev/null
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_plane_plus_line_policies.h
@@ -0,0 +1,58 @@
+// Copyright (c) 2025  GeometryFactory (France). 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)     : Leo Valque
+
+#ifndef CGAL_SURFACE_MESH_SIMPLIFICATION_POLICIES_GARLANDHECKBERT_PLANE_PLUS_LINE_POLICIES_H
+#define CGAL_SURFACE_MESH_SIMPLIFICATION_POLICIES_GARLANDHECKBERT_PLANE_PLUS_LINE_POLICIES_H
+
+#include <CGAL/license/Surface_mesh_simplification.h>
+
+#include <CGAL/Surface_mesh_simplification/internal/Common.h>
+#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_policy_base.h>
+#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_functions.h>
+
+#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_composed_policies.h>
+#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_plane_policies.h>
+#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_line_policies.h>
+
+namespace CGAL {
+namespace Surface_mesh_simplification {
+
+template<typename TriangleMesh, typename GeomTraits>
+class GarlandHeckbert_plane_plus_line_policies
+  : public GarlandHeckbert_composed_policies<TriangleMesh, GeomTraits,
+                                             GarlandHeckbert_plane_policies<TriangleMesh, GeomTraits>,
+                                             GarlandHeckbert_line_policies<TriangleMesh, GeomTraits> >
+{
+  typedef GarlandHeckbert_composed_policies<TriangleMesh, GeomTraits,
+                                             GarlandHeckbert_plane_policies<TriangleMesh, GeomTraits>,
+                                             GarlandHeckbert_line_policies<TriangleMesh, GeomTraits> > Base;
+
+public:
+  typedef typename Base::Quadric_calculator Quadric_calculator;
+
+  typedef typename GeomTraits::FT                                              FT;
+
+public:
+  GarlandHeckbert_plane_plus_line_policies(TriangleMesh& tmesh,
+                                           const FT dm = FT(100),
+                                           const FT line_weight=FT(0.01))
+    : Base(tmesh, FT(1.)/line_weight, dm)
+  { }
+
+public:
+  using Base::operator();
+  using Base::get_cost;
+  using Base::get_placement;
+};
+
+} // namespace Surface_mesh_simplification
+} // namespace CGAL
+
+#endif // CGAL_SURFACE_MESH_SIMPLIFICATION_POLICIES_GARLANDHECKBERT_PLANE_PLUS_LINE_POLICIES_H
\ No newline at end of file
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_policies.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_policies.h
index c45bfe2a65f..b2404bb613e 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_policies.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_policies.h
@@ -21,12 +21,15 @@
 #include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_triangle_policies.h>
 #include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_plane_policies.h>
 #include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_triangle_policies.h>
+#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_line_policies.h>
+#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_composed_policies.h>
+#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_plane_plus_line_policies.h>
 
 namespace CGAL {
 namespace Surface_mesh_simplification {
 
 template<typename TriangleMesh, typename GeomTraits>
-using GarlandHeckbert_policies CGAL_DEPRECATED = GarlandHeckbert_plane_policies<TriangleMesh, GeomTraits>;
+using GarlandHeckbert_policies = GarlandHeckbert_plane_plus_line_policies<TriangleMesh, GeomTraits>;
 
 } // namespace Surface_mesh_simplification
 } // namespace CGAL