diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Complex_cells_selector.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Complex_cells_selector.h
new file mode 100644
index 00000000000..d7822d6bea0
--- /dev/null
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/Complex_cells_selector.h
@@ -0,0 +1,45 @@
+// Copyright (c) 2024 GeometryFactory (France) and Telecom Paris (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)     : Jane Tournois, Noura Faraj, Jean-Marc Thiery, Tamy Boubekeur
+
+#ifndef CGAL_INTERNAL_C3T3_CELLS_SELECTOR_H
+#define CGAL_INTERNAL_C3T3_CELLS_SELECTOR_H
+
+#include <CGAL/license/Tetrahedral_remeshing.h>
+
+#include <CGAL/property_map.h>
+
+namespace CGAL
+{
+namespace Tetrahedral_remeshing
+{
+  template<typename Tr>
+  struct Complex_cells_selector
+  {
+    using key_type = typename Tr::Cell_handle;
+    using value_type = bool;
+    using reference = bool;
+    using category = boost::read_write_property_map_tag;
+
+    friend value_type get(const Complex_cells_selector&, const key_type& c)
+    {
+      using SI = typename Tr::Cell::Subdomain_index;
+      return c->subdomain_index() != SI();
+    }
+    friend void put(Complex_cells_selector&, const key_type&, const value_type)
+    {} //nothing to do : subdomain indices are updated in remeshing};
+  };
+
+
+} // end namespace Tetrahedral_remeshing
+} // end namespace CGAL
+
+#endif // CGAL_INTERNAL_C3T3_CELLS_SELECTOR_H
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/peel_slivers.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/peel_slivers.h
index 9cbff2ba95a..183e53a000d 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/peel_slivers.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/peel_slivers.h
@@ -16,11 +16,15 @@
 #include <CGAL/license/Tetrahedral_remeshing.h>
 
 #include <CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h>
+#include <CGAL/Tetrahedral_remeshing/Complex_cells_selector.h>
 
 namespace CGAL
 {
 namespace Tetrahedral_remeshing
 {
+template<typename C3T3>
+std::size_t peel_slivers(C3T3& c3t3,
+                         const typename C3T3::Triangulation::Geom_traits::FT& sliver_angle);
 
 template<typename C3T3, typename CellSelector>
 std::size_t peel_slivers(C3T3& c3t3,
@@ -41,7 +45,8 @@ std::size_t peel_slivers(C3T3& c3t3,
 #endif
   for (Cell_handle cit : c3t3.cells_in_complex())
   {
-    if(!get(cell_selector, cit))
+    const bool selected = get(cell_selector, cit);
+    if(!selected)
       continue;
 
     std::array<bool, 4> facets_on_surface;
@@ -111,6 +116,16 @@ std::size_t peel_slivers(C3T3& c3t3,
   return nb_slivers_peel;
 }
 
+template<typename C3T3>
+std::size_t peel_slivers(C3T3 & c3t3,
+  const typename C3T3::Triangulation::Geom_traits::FT & sliver_angle)
+{
+  using Tr = typename C3T3::Triangulation;
+  return peel_slivers(c3t3, sliver_angle,
+    CGAL::Tetrahedral_remeshing::Complex_cells_selector<Tr>());
+}
+
+
 } // end namespace Tetrahedral_remeshing
 } // end namespace CGAL
 
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_adaptive_remeshing_impl.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_adaptive_remeshing_impl.h
index 5912bb67575..1e465f2c3b6 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_adaptive_remeshing_impl.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_adaptive_remeshing_impl.h
@@ -57,22 +57,7 @@ public:
   void after_flip(CellHandle /* c */) {}
 };
 
-template<typename Tr>
-struct All_cells_selected
-{
-  using key_type = typename Tr::Cell_handle;
-  using value_type = bool;
-  using reference = bool;
-  using category = boost::read_write_property_map_tag;
 
-  friend value_type get(const All_cells_selected&, const key_type& c)
-  {
-    using SI = typename Tr::Cell::Subdomain_index;
-    return c->subdomain_index() != SI();
-  }
-  friend void put(All_cells_selected&, const key_type&, const value_type)
-  {} //nothing to do : subdomain indices are updated in remeshing};
-};
 
 
 template<typename Triangulation
diff --git a/Tetrahedral_remeshing/include/CGAL/tetrahedral_remeshing.h b/Tetrahedral_remeshing/include/CGAL/tetrahedral_remeshing.h
index 451cab5ee57..7e4acbf9b5b 100644
--- a/Tetrahedral_remeshing/include/CGAL/tetrahedral_remeshing.h
+++ b/Tetrahedral_remeshing/include/CGAL/tetrahedral_remeshing.h
@@ -20,6 +20,8 @@
 
 #include <CGAL/Tetrahedral_remeshing/Sizing_field.h>
 #include <CGAL/Tetrahedral_remeshing/Uniform_sizing_field.h>
+#include <CGAL/Tetrahedral_remeshing/Complex_cells_selector.h>
+
 #include <CGAL/Tetrahedral_remeshing/internal/tetrahedral_adaptive_remeshing_impl.h>
 #include <CGAL/Tetrahedral_remeshing/internal/compute_c3t3_statistics.h>
 
@@ -228,11 +230,11 @@ void tetrahedral_isotropic_remeshing(
   typedef typename internal_np::Lookup_named_param_def <
     internal_np::cell_selector_t,
     NamedParameters,
-    Tetrahedral_remeshing::internal::All_cells_selected<Tr>//default
+    Tetrahedral_remeshing::Complex_cells_selector<Tr>//default
   > ::type SelectionFunctor;
   SelectionFunctor cell_select
     = choose_parameter(get_parameter(np, internal_np::cell_selector),
-                       Tetrahedral_remeshing::internal::All_cells_selected<Tr>());
+                       Tetrahedral_remeshing::Complex_cells_selector<Tr>());
 
   typedef typename Tr::Vertex_handle Vertex_handle;
   typedef typename internal_np::Lookup_named_param_def <
@@ -485,11 +487,11 @@ void tetrahedral_isotropic_remeshing(
   typedef typename internal_np::Lookup_named_param_def <
               internal_np::cell_selector_t,
               NamedParameters,
-              Tetrahedral_remeshing::internal::All_cells_selected<Tr>//default
+              Tetrahedral_remeshing::Complex_cells_selector<Tr>//default
               > ::type SelectionFunctor;
   SelectionFunctor cell_select
     = choose_parameter(get_parameter(np, internal_np::cell_selector),
-                       Tetrahedral_remeshing::internal::All_cells_selected<Tr>());
+                       Tetrahedral_remeshing::Complex_cells_selector<Tr>());
 
   typedef typename Tr::Vertex_handle Vertex_handle;
   typedef typename internal_np::Lookup_named_param_def <