diff --git a/Bounding_volumes/doc/Bounding_volumes/PackageDescription.txt b/Bounding_volumes/doc/Bounding_volumes/PackageDescription.txt
index 6fa63e9c60d..7ec2b717b7b 100644
--- a/Bounding_volumes/doc/Bounding_volumes/PackageDescription.txt
+++ b/Bounding_volumes/doc/Bounding_volumes/PackageDescription.txt
@@ -20,12 +20,6 @@
 \cgalPkgShortInfoEnd
 \cgalPkgDescriptionEnd
 
-\cgalCRPSection{Assertions}
-
-The optimization code uses infix `OPTIMISATION` in the assertions,
-e.g. defining the compiler flag
-`CGAL_OPTIMISATION_NO_PRECONDITIONS` switches precondition
-checking off, cf. Section  \ref secchecks.
 
 \cgalClassifedRefPages
 
@@ -62,4 +56,3 @@ checking off, cf. Section  \ref secchecks.
 - `CGAL::Min_sphere_of_spheres_d<Traits>`
 - `MinSphereOfSpheresTraits`
 */
-
diff --git a/Documentation/doc/Documentation/Developer_manual/Chapter_checks.txt b/Documentation/doc/Documentation/Developer_manual/Chapter_checks.txt
index 1a6fb78e4cb..209aeca5649 100644
--- a/Documentation/doc/Documentation/Developer_manual/Chapter_checks.txt
+++ b/Documentation/doc/Documentation/Developer_manual/Chapter_checks.txt
@@ -156,53 +156,8 @@ the computation is done with some exact number type.
 \section secchecks_controlling Controlling checks at a finer granularity
 
 The macros and related compile-time flags described so far all operate
-on the whole library. Sometimes the user may want to have a more
-selective control.  \cgal offers the possibility to turn checks on
-and off on a per-package basis. Therefore a package-specific term is
-inserted in the macro names directly after the \cgal prefix,
-<I>e.g.</I>, `CGAL_kernel_assertion(<Cond>)`. Similarly, the uppercase
-term is used for the compile-time flags;
-<I>e.g.</I>, `CGAL_KERNEL_NO_WARNINGS` switches off the warnings
-in <I>only</I> the kernel. Other packages have their own specific
-terms as documented in the corresponding chapters of the
-reference manual.
-
-For a new package you will first have to create a suitable header file
-with all macro definitions.  This is done with the shell script
-<TT>cgal_create_assertions.sh</TT>, to be found in the
-<TT>scripts</TT> directory.
-
-The following command will create a file <TT>optimisation_assertions.h</TT>:
-
-<CENTER>
-  <TT>sh cgal_create_assertions.sh optimisation</TT>
-
-</CENTER>
-
-You should place the generated file in the proper directory (and possibly
-rename it).  Then you can use the checks in the following fashion.
-
-\code{.cpp}
- #include <CGAL/Optimisation/assertions.h>
-
- void optimisation_foo( int i)
- {
-   CGAL_optimisation_precondition_msg( i == 42, "Only 42 allowed!");
-   // ...
- }
-\endcode
-
-The documentation of your new package has to name the term chosen to be
-part of the package-specific macros in
-order to enable the user to selectively turn off and on the checks of
-your package. For example, in the documentation of the optimisation
-package you can find a sentence similar to the following.
-<BLOCKQUOTE>
-  The optimisation code uses the term OPTIMISATION for the checks;
-  <I>e.g.</I>, setting the compile time flag
-  `CGAL_OPTIMISATION_NO_PRECONDITIONS` switches off precondition
-  checking in the optimisation code.
-</BLOCKQUOTE>
+on the whole library.  \cgal offers the possibility to turn checks on
+and off just for the kernel.
 
 \section secchecks_cgal_assume Suppress warnings using CGAL_assume.
 
diff --git a/Mesh_2/include/CGAL/Constrained_voronoi_diagram_2.h b/Mesh_2/include/CGAL/Constrained_voronoi_diagram_2.h
index b03ca56d811..eb61e4bf50a 100644
--- a/Mesh_2/include/CGAL/Constrained_voronoi_diagram_2.h
+++ b/Mesh_2/include/CGAL/Constrained_voronoi_diagram_2.h
@@ -21,6 +21,7 @@
 #include <stack>
 #include <CGAL/iterator.h>
 #include <CGAL/tuple.h>
+#include <CGAL/assertions.h>
 #include <CGAL/Kernel/global_functions_2.h>
 
 namespace CGAL {
@@ -415,8 +416,8 @@ template<typename Tr>
 Cvd_cell_2<Tr> dual(const Tr& tr,
                     const typename Tr::Vertex_handle& v)
 {
-  CGAL_triangulation_precondition( v != typename Tr::Vertex_handle());
-  CGAL_triangulation_precondition( !tr.is_infinite(v));
+  CGAL_precondition( v != typename Tr::Vertex_handle());
+  CGAL_precondition( !tr.is_infinite(v));
 
   Constrained_voronoi_diagram_2<Tr> diagram(tr);
   return diagram.cvd_cell(v);
@@ -436,8 +437,8 @@ Cvd_cell_2<Tr> dual(const Tr& tr,
 //  typedef Tr::Geom_traits::Ray_2    Ray;
 //  typedef Tr::Geom_traits::Vector_2 Vector_2;
 //
-//  CGAL_triangulation_precondition( v != Vertex_handle());
-//  CGAL_triangulation_precondition( !tr.is_infinite(v));
+//  CGAL_precondition( v != Vertex_handle());
+//  CGAL_precondition( !tr.is_infinite(v));
 //
 //  // The Circulator moves ccw.
 //  std::vector<Segment> segments;
diff --git a/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h b/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h
index 1a13e725a44..e8f105cd241 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h
@@ -568,7 +568,7 @@ refine_mesh(std::string dump_after_refine_surface_prefix)
   std::cerr << "Total refining surface time: " << timer.time() << "s" << std::endl;
   std::cerr << std::endl;
 
-  CGAL_triangulation_postcondition(r_tr.is_valid());
+  CGAL_postcondition(r_tr.is_valid());
 
   elapsed_time += timer.time();
   timer.stop(); timer.reset(); timer.start();
@@ -613,7 +613,7 @@ refine_mesh(std::string dump_after_refine_surface_prefix)
   std::cerr << "Total refining time: " << timer.time()+elapsed_time << "s" << std::endl;
   std::cerr << std::endl;
 
-  CGAL_triangulation_postcondition(r_tr.is_valid());
+  CGAL_postcondition(r_tr.is_valid());
 #endif
 
   (void)(forced_stop()); // sets *error_code