diff --git a/Bounding_volumes/test/Bounding_volumes/min_sphere_test.cpp b/Bounding_volumes/test/Bounding_volumes/min_sphere_test.cpp
index 82b71269443..ff82ea1bdb0 100644
--- a/Bounding_volumes/test/Bounding_volumes/min_sphere_test.cpp
+++ b/Bounding_volumes/test/Bounding_volumes/min_sphere_test.cpp
@@ -33,10 +33,12 @@
 #include <CGAL/Random.h>
 #include <CGAL/Cartesian_d.h>
 #include <CGAL/Homogeneous_d.h>
-#include <sstream>
-#include <cassert>
 #include <CGAL/Min_sphere_annulus_d_traits_d.h>
 #include <CGAL/Min_sphere_d.h>
+#include <CGAL/Quotient.h>
+
+#include <cassert>
+#include <sstream>
 
 using namespace CGAL;
 
diff --git a/Cartesian_kernel/include/CGAL/Cartesian_converter.h b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
index 65a68c612fb..946dc51ce4b 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian_converter.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
@@ -39,6 +39,8 @@
 #include <boost/mpl/logical.hpp>
 #include <boost/mpl/remove.hpp>
 
+#include <type_traits>
+
 namespace CGAL {
 
 // Guess which compiler needs this work around ?
@@ -82,8 +84,7 @@ struct Converting_visitor : boost::static_visitor<> {
 } // namespace internal
 
 template < class K1, class K2,
-//          class Converter = NT_converter<typename K1::FT, typename K2::FT> >
-           class Converter>
+           class Converter /*= typename internal::Default_converter<K1, K2>::Type*/>
 class Cartesian_converter : public Enum_converter
 {
     typedef Enum_converter   Base;
@@ -96,24 +97,24 @@ public:
     using Base::operator();
 
     Origin
-    operator()(const Origin& o) const
+    operator()(Origin o) const
     {
         return o;
     }
 
     Null_vector
-    operator()(const Null_vector& n) const
+    operator()(Null_vector n) const
     {
         return n;
     }
 
-    Bbox_2
+    const Bbox_2&
     operator()(const Bbox_2& b) const
     {
         return b;
     }
 
-    Bbox_3
+    const Bbox_3&
     operator()(const Bbox_3& b) const
     {
         return b;
@@ -125,6 +126,14 @@ public:
         return c(a);
     }
 
+    template <typename T>
+    T
+    operator()(const T t,
+               typename std::enable_if<std::is_fundamental<T>::value>::type* = nullptr) const
+    {
+        return t;
+    }
+
     // drop the boost::detail::variant::void_ generated by the macros
     // from the sequence, transform with the type mapper and throw the
     // new list into a variant
@@ -384,24 +393,25 @@ public:
       return std::make_pair(operator()(pp.first), operator()(pp.second));
     }
 
-    typename K2::Aff_transformation_3
-    operator()(const typename K1::Aff_transformation_3 &a) const
+    typename K2::Aff_transformation_2
+    operator()(const typename K1::Aff_transformation_2& a) const
     {
-        typedef typename K2::Aff_transformation_3 Aff_transformation_3;
-      typename K2::FT t[12];
-      for(int i=0; i< 3; ++i)
-      {
-        for(int j=0; j<4; ++j)
-        {
-          t[i*4+j] = a.m(i,j);
-        }
-      }
-      return Aff_transformation_3(
-            t[0],t[1],t[2],t[3],
-            t[4],t[5],t[6],t[7],
-            t[8],t[9],t[10],t[11],
-            a.m(3,3));
+      typedef typename K2::Aff_transformation_2 Aff_transformation_2;
+      return Aff_transformation_2(c(a.m(0,0)), c(a.m(0,1)), c(a.m(0,2)),
+                                  c(a.m(1,0)), c(a.m(1,1)), c(a.m(1,2)),
+                                  c(a.m(2,2)));
     }
+
+    typename K2::Aff_transformation_3
+    operator()(const typename K1::Aff_transformation_3& a) const
+    {
+      typedef typename K2::Aff_transformation_3 Aff_transformation_3;
+      return Aff_transformation_3(c(a.m(0,0)), c(a.m(0,1)), c(a.m(0,2)), c(a.m(0,3)),
+                                  c(a.m(1,0)), c(a.m(1,1)), c(a.m(1,2)), c(a.m(1,3)),
+                                  c(a.m(2,0)), c(a.m(2,1)), c(a.m(2,2)), c(a.m(2,3)),
+                                  c(a.m(3,3)));
+    }
+
 private:
     Converter c;
     K2 k;
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h b/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
index 601d9ac504f..22edf4e3e18 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
@@ -28,6 +28,9 @@
 #include <CGAL/Enum_converter.h>
 #include <CGAL/Bbox_2.h>
 #include <CGAL/Bbox_3.h>
+#include <CGAL/Origin.h>
+
+#include <type_traits>
 
 namespace CGAL {
 
@@ -47,13 +50,25 @@ public:
 
     using Base::operator();
 
-    Bbox_2
+    Origin
+    operator()(Origin o) const
+    {
+        return o;
+    }
+
+    Null_vector
+    operator()(Null_vector n) const
+    {
+        return n;
+    }
+
+    const Bbox_2&
     operator()(const Bbox_2& b)
     {
         return b;
     }
 
-    Bbox_3
+    const Bbox_3&
     operator()(const Bbox_3& b)
     {
         return b;
@@ -62,13 +77,21 @@ public:
     typename K2::RT
     operator()(const typename K1::RT &a) const
     {
-        return c(a);
+        return rc(a);
     }
 
     typename K2::FT
     operator()(const typename K1::FT &a) const
     {
-        return c(a);
+        return fc(a);
+    }
+
+    template <typename T>
+    T
+    operator()(const T t,
+               typename std::enable_if<std::is_fundamental<T>::value>::type* = nullptr) const
+    {
+        return t;
     }
 
     typename K2::Point_2
diff --git a/Kernel_23/test/Kernel_23/test_converter.cpp b/Kernel_23/test/Kernel_23/test_converter.cpp
new file mode 100644
index 00000000000..8a94f9845cf
--- /dev/null
+++ b/Kernel_23/test/Kernel_23/test_converter.cpp
@@ -0,0 +1,76 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Simple_cartesian.h>
+#include <CGAL/Simple_homogeneous.h>
+#include <CGAL/Interval_nt.h>
+
+#include <CGAL/Cartesian_converter.h>
+#include <CGAL/Homogeneous_converter.h>
+
+#ifdef CGAL_USE_CORE
+#include <CGAL/CORE_Expr.h>
+#endif
+
+#include <iostream>
+
+int main()
+{
+  using EPICK = CGAL::Exact_predicates_inexact_constructions_kernel;
+  using EPECK = CGAL::Exact_predicates_exact_constructions_kernel;
+  using SCLD = CGAL::Simple_cartesian<long double>;
+  using SCI = CGAL::Simple_cartesian<CGAL::Interval_nt<> >;
+  using SHI = CGAL::Simple_homogeneous<CGAL::Interval_nt<> >;
+  using NT_exact = CGAL::internal::Exact_field_selector<double>::Type;
+  using SHD = CGAL::Simple_homogeneous<double>;
+  using SHE = CGAL::Simple_homogeneous<NT_exact>;
+
+  CGAL::Cartesian_converter<SCI, EPICK> sci_to_epick;
+  CGAL::Cartesian_converter<SCLD, EPICK> scld_to_epick;
+  CGAL::Cartesian_converter<SCI, EPECK> sci_to_epeck;
+  CGAL::Cartesian_converter<EPECK, EPICK> epeck_to_epick;
+  CGAL::Homogeneous_converter<SHI, SHD> shi_to_shd;
+  CGAL::Homogeneous_converter<SHE, SHD> she_to_shd;
+  CGAL::Homogeneous_converter<SHE, SHE> she_to_she;
+
+  assert(sci_to_epick(SCI::FT(2)) == EPICK::FT(2));
+  assert(scld_to_epick((long double)(2.)) /*long double is FT*/ == EPICK::FT(2));
+
+  // fundamental types != FT
+  assert(sci_to_epick((long int)(2)) == (long int)(2));
+  assert(sci_to_epick(2.) == 2.);
+  assert(sci_to_epick(bool(true)) == true);
+  assert(sci_to_epick(true) == true);
+  assert(sci_to_epick(false) == false);
+  assert(sci_to_epick(CGAL::ON_POSITIVE_SIDE) == CGAL::ON_POSITIVE_SIDE);
+
+#ifdef CGAL_USE_CORE
+  using SSCE = CGAL::Simple_cartesian<CORE::Expr>;
+  CGAL::Cartesian_converter<SSCE, EPICK> scce_to_epick;
+
+  assert(scce_to_epick(2.) == 2.);
+  assert(scce_to_epick((signed long long int)(1)) == 1);
+  scce_to_epick(CORE::Expr(2.) == EPICK::FT(2));
+#endif
+
+  assert(sci_to_epeck((signed char)('a')) == (signed char)('a'));
+
+  assert(epeck_to_epick(EPECK::FT(2)) == EPICK::FT(2));
+  assert(epeck_to_epick(2.) == 2.);
+
+  // Homogeneous
+  assert(shi_to_shd(2.) == 2.);
+  assert(shi_to_shd(SHI::RT(2.)) == SHD::RT(2.));
+
+  assert(she_to_shd(SHE::RT(2)) == SHD::RT(2));
+  assert(she_to_shd(SHE::FT(2.)) == SHD::FT(2.));
+  assert(she_to_shd(2.) == 2.);
+  assert(she_to_she(SHE::RT(2)) == SHE::RT(2));
+
+  std::cout << "NT_exact is " << typeid(NT_exact).name() << std::endl;
+  CGAL::NT_converter<CGAL::Quotient<NT_exact>, CGAL::Quotient<NT_exact> > qnte_to_qnte;
+  assert(qnte_to_qnte(2.) == CGAL::Quotient<NT_exact>(2.));
+
+  std::cout << "Done" << std::endl;
+
+  return EXIT_SUCCESS;
+}
diff --git a/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h b/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h
index a136b3da81d..e38fea77163 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h
@@ -82,13 +82,13 @@ public:
         : c(), k(), result_point_(20) {}
 
     Origin
-    operator()(const Origin& o) const
+    operator()(Origin o) const
     {
         return o;
     }
 
     Null_vector
-    operator()(const Null_vector& n) const
+    operator()(Null_vector n) const
     {
         return n;
     }
@@ -99,6 +99,14 @@ public:
         return c(a);
     }
 
+    template <typename T>
+    T
+    operator()(const T t,
+               typename std::enable_if<std::is_fundamental<T>::value>::type* = nullptr) const
+    {
+        return t;
+    }
+
     std::vector<Object>
     operator()(const std::vector<Object>& v) const
     {
@@ -110,11 +118,6 @@ public:
       return res;
     }
 
-    int operator()(const int &a)
-    {
-        return a;
-    }
-
     typename K2::Point_d
     operator()(const typename K1::Point_d &a) const
     {
diff --git a/Number_types/include/CGAL/NT_converter.h b/Number_types/include/CGAL/NT_converter.h
index ac225f1e0cb..37f259abf80 100644
--- a/Number_types/include/CGAL/NT_converter.h
+++ b/Number_types/include/CGAL/NT_converter.h
@@ -13,16 +13,20 @@
 #ifndef CGAL_NT_CONVERTER_H
 #define CGAL_NT_CONVERTER_H
 
-#include <functional>
 #include <CGAL/number_type_config.h>
 #include <CGAL/number_utils.h>
 
-template <bool> class Interval_nt;
+#include <functional>
 
 namespace CGAL {
 
-// A number type converter usable as default, using the conversion operator.
+template <bool>
+class Interval_nt;
 
+template <class NT>
+class Quotient;
+
+// A number type converter usable as default, using the conversion operator.
 template < class NT1, class NT2 >
 struct NT_converter
   : public CGAL::cpp98::unary_function< NT1, NT2 >
@@ -38,6 +42,7 @@ struct NT_converter
 // - double to call to_double().
 // - Interval_nt<> to call to_interval().
 // - NT1 == NT2 to return a reference instead of copying.
+// - Quotient conversions
 
 template < class NT1 >
 struct NT_converter < NT1, NT1 >
@@ -116,6 +121,29 @@ struct NT_converter < Interval_nt<b>, Interval_nt<b> >
     }
 };
 
+template < class NT >
+struct NT_converter < Quotient<NT>, Quotient<NT> >
+  : public CGAL::cpp98::unary_function< Quotient<NT>, Quotient<NT> >
+{
+    const Quotient<NT>&
+    operator()(const Quotient<NT> & q) const
+    {
+        return q;
+    }
+};
+
+template < class NT1, class NT2 >
+struct NT_converter < Quotient<NT1>, Quotient<NT2> >
+  : public CGAL::cpp98::unary_function< Quotient<NT1>, Quotient<NT2> >
+{
+    Quotient<NT2>
+    operator()(const Quotient<NT1> & q) const
+    {
+        NT_converter < NT1, NT2 > nt;
+        return Quotient<NT2>(nt(q.numerator()), nt(q.denominator()));
+    }
+};
+
 } //namespace CGAL
 
 #endif // CGAL_NT_CONVERTER_H