diff --git a/STL_Extension/include/CGAL/Named_function_parameters.h b/STL_Extension/include/CGAL/Named_function_parameters.h
index 61974cf4bb9..1daa82ed9e8 100644
--- a/STL_Extension/include/CGAL/Named_function_parameters.h
+++ b/STL_Extension/include/CGAL/Named_function_parameters.h
@@ -440,7 +440,7 @@ inline all_default()
 }
 #endif
 
-template <class Tag, bool ref_only = false>
+template <class Tag, bool ref_only = false, bool ref_is_const = false>
 struct Boost_parameter_compatibility_wrapper
 {
   template <typename K>
@@ -461,7 +461,7 @@ struct Boost_parameter_compatibility_wrapper
 };
 
 template <class Tag>
-struct Boost_parameter_compatibility_wrapper<Tag, true>
+struct Boost_parameter_compatibility_wrapper<Tag, true, true>
 {
   template <typename K>
   Named_function_parameters<std::reference_wrapper<const K>, Tag>
@@ -478,7 +478,11 @@ struct Boost_parameter_compatibility_wrapper<Tag, true>
     typedef Named_function_parameters<std::reference_wrapper<const K>, Tag> Params;
     return Params(std::cref(p));
   }
+};
 
+template <class Tag>
+struct Boost_parameter_compatibility_wrapper<Tag, true, false>
+{
   template <typename K>
   Named_function_parameters<std::reference_wrapper<K>, Tag>
   operator()(K& p) const
@@ -509,9 +513,9 @@ struct Boost_parameter_compatibility_wrapper<Tag, true>
 #define CGAL_add_named_parameter_with_compatibility(X, Y, Z)        \
   const Boost_parameter_compatibility_wrapper<internal_np::X> Z;
 #define CGAL_add_named_parameter_with_compatibility_cref_only(X, Y, Z)        \
-  const Boost_parameter_compatibility_wrapper<internal_np::X, true> Z;
+  const Boost_parameter_compatibility_wrapper<internal_np::X, true, true> Z;
 #define CGAL_add_named_parameter_with_compatibility_ref_only(X, Y, Z)        \
-  const Boost_parameter_compatibility_wrapper<internal_np::X, true> Z;
+  const Boost_parameter_compatibility_wrapper<internal_np::X, true, false> Z;
 #define CGAL_add_extra_named_parameter_with_compatibility(X, Y, Z)        \
   const Boost_parameter_compatibility_wrapper<internal_np::X> Z;
 #include <CGAL/STL_Extension/internal/parameters_interface.h>
diff --git a/Scripts/developer_scripts/test_merge_of_branch b/Scripts/developer_scripts/test_merge_of_branch
index f0ddcbc36fd..cdf1070fa87 100755
--- a/Scripts/developer_scripts/test_merge_of_branch
+++ b/Scripts/developer_scripts/test_merge_of_branch
@@ -220,9 +220,9 @@ git_dir=`pwd`
 tmp_dir=`mktemp -d`
 cd $tmp_dir
 echo $tmp_dir
-echo "#include <CGAL/Named_function_parameters.h>\nstruct A{};\nint main(){" > main.cpp
+echo "#include <CGAL/Named_function_parameters.h>\nstruct A{};\nint main(){\nA a;\n" > main.cpp
 for i in `echo $nps`; do
-  echo "  CGAL::parameters::${i}(A()).${i}(A());" >> main.cpp
+  echo "  CGAL::parameters::${i}(a).${i}(a);" >> main.cpp
 done
 echo "}" >> main.cpp
 if ! g++ -DCGAL_NO_STATIC_ASSERTION_TESTS -I$git_dir/STL_Extension/include -I$git_dir/Stream_support/include -I$git_dir/Installation/include main.cpp; then