diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Mesh_3/Poisson_mesh_traits_generator_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Mesh_3/Poisson_mesh_traits_generator_3.h
new file mode 100644
index 00000000000..b92b6488db8
--- /dev/null
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Mesh_3/Poisson_mesh_traits_generator_3.h
@@ -0,0 +1,45 @@
+// Copyright (c) 2006-2007, 2024  INRIA Sophia-Antipolis (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)     : Laurent Rineau, Jane Tournois
+
+#ifndef CGAL_MESH_3_POISSON_MESH_TRAITS_GENERATOR_3_H
+#define CGAL_MESH_3_POISSON_MESH_TRAITS_GENERATOR_3_H
+
+#include <CGAL/license/Poisson_surface_reconstruction_3.h>
+
+
+#include <CGAL/Surface_mesher/Poisson_sphere_oracle_3.h>
+
+namespace CGAL {
+
+template <class K>
+class Sphere_3;
+
+/** Default traits class.
+ *  Partial specialization will be in other headers
+*/
+template <typename Surface>
+struct Poisson_mesh_traits_generator_3
+{
+  typedef typename Surface::Surface_mesher_traits_3 Type;
+  typedef Type type; // for Boost compatibility (meta-programming)
+};
+
+  // specialization for Kernel::Sphere_3
+template <typename Kernel>
+struct Poisson_mesh_traits_generator_3<CGAL::Sphere_3<Kernel> >
+{
+  typedef Surface_mesher::Poisson_sphere_oracle_3<Kernel> Type;
+  typedef Type type; // for Boost compatibility (meta-programming)
+};
+
+} // end namespace CGAL
+
+#endif // CGAL_MESH_3_POISSON_MESH_TRAITS_GENERATOR_3_H
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Surface_mesher/Poisson_implicit_surface_oracle_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Surface_mesher/Poisson_implicit_surface_oracle_3.h
index e43214ce663..5ebd27391d8 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Surface_mesher/Poisson_implicit_surface_oracle_3.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Surface_mesher/Poisson_implicit_surface_oracle_3.h
@@ -17,9 +17,8 @@
 #include <CGAL/license/Poisson_surface_reconstruction_3.h>
 
 
-#include <CGAL/Surface_mesher/Null_oracle_visitor.h>
 #include <CGAL/point_generators_3.h>
-#include <CGAL/Surface_mesher/Sphere_oracle_3.h>
+#include <CGAL/Surface_mesher/Poisson_sphere_oracle_3.h>
 #include <CGAL/Surface_mesher/Implicit_surface_oracle_3.h>
 #include <CGAL/Real_embeddable_traits.h>
 #include <CGAL/squared_distance_3.h>
@@ -56,7 +55,7 @@ namespace CGAL {
       Return_min<typename Transform_functor_::result_type>,
     class Point_creator = Creator_uniform_3<typename GT::FT,
                                             typename GT::Point_3>,
-    class Visitor = Null_oracle_visitor
+    class Visitor = Poisson_null_oracle_visitor
     >
   class Poisson_implicit_surface_oracle_3
   {
@@ -68,7 +67,7 @@ namespace CGAL {
                                       Point_creator,
                                       Visitor> Self;
 
-    typedef Sphere_oracle_3<GT, Point_creator> Sphere_oracle;
+    typedef Poisson_sphere_oracle_3<GT, Point_creator> Sphere_oracle;
 
     typedef typename GT::Point_3 Point;
 
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/poisson_refine_triangulation.h b/Poisson_surface_reconstruction_3/include/CGAL/poisson_refine_triangulation.h
index c103468f3f1..13f08e45727 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/poisson_refine_triangulation.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/poisson_refine_triangulation.h
@@ -21,7 +21,7 @@
 #include <CGAL/Mesh_3/Poisson_refine_cells_3.h>
 #include <CGAL/Poisson_mesh_cell_criteria_3.h>
 #include <CGAL/assertions.h>
-#include <CGAL/Surface_mesh_traits_generator_3.h>
+#include <CGAL/Mesh_3/Poisson_mesh_traits_generator_3.h>
 
 namespace CGAL {
 
@@ -142,7 +142,7 @@ class Poisson_mesher_level_impl_base :
 template <typename Tr,
           typename Criteria,
           typename Surface,
-          typename Oracle = typename CGAL::Surface_mesh_traits_generator_3<Surface>::type,
+          typename Oracle = typename CGAL::Poisson_mesh_traits_generator_3<Surface>::type,
           typename PreviousLevel = Null_mesher_level
  >
 class Poisson_mesher_level :
@@ -220,7 +220,7 @@ unsigned int poisson_refine_triangulation(
     , Sizing_field
     , Second_sizing_field
     > Tets_criteria;
-  typedef typename CGAL::Surface_mesh_traits_generator_3<Surface>::type Oracle;
+  typedef typename CGAL::Poisson_mesh_traits_generator_3<Surface>::type Oracle;
   typedef Poisson_mesher_level<Tr, Tets_criteria, Surface, Oracle, Null_mesher_level> Refiner;