diff --git a/Cartesian_kernel/include/CGAL/Cartesian_converter.h b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
index 096e0b4831b..d87dcac6610 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian_converter.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
@@ -126,7 +126,7 @@ public:
         return c(a);
     }
 
-    // This intentionally does not check that K1::FT is constructible from T, because otherwise
+    // This intentionally does not require that K1::FT is constructible from T, because otherwise
     // the function `bool Enum_converter::operator()(bool)` might be called instead, with an implicit
     // conversion from the fundamental type to bool, which is usually unintended.
     template <typename T>
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h b/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
index 25391d6097a..9d844278427 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
@@ -86,7 +86,7 @@ public:
         return fc(a);
     }
 
-    // This intentionally does not check that K1::RT is constructible from T, because otherwise
+    // This intentionally does not require that K1::RT is constructible from T, because otherwise
     // the function `bool Enum_converter::operator()(bool)` might be called instead, with an implicit
     // conversion from the fundamental type to bool, which is usually unintended.
     template <typename T>
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..0acf4647406
--- /dev/null
+++ b/Kernel_23/test/Kernel_23/test_converter.cpp
@@ -0,0 +1,69 @@
+#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 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<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;
+
+  assert(sci_to_epick(SCI::FT(2)) == EPICK::FT(2));
+  assert(sci_to_epick((long int)(2)) == EPICK::FT(2)); // long int --> SCI::FT --> EPICK::FT
+  assert(sci_to_epick(2.) == EPICK::FT(2)); // double --> SCI::FT --> EPICK::FT
+  assert(sci_to_epick(bool(2.)) == true);
+
+#ifdef CGAL_USE_CORE
+  using SSCE = CGAL::Simple_cartesian<CORE::Expr>;
+  CGAL::Cartesian_converter<SSCE, EPICK> scce_to_epick;
+
+  // double is a fundamental type, but CORE::Expr has no implicit double --> CORE::Expr conversion
+  assert(scce_to_epick(2) == EPICK::FT(2));
+
+  // This does not compile because 'signed long long int' is a fundamental type,
+  // but there is no CORE::Expr(signed long long int) constructor
+//  assert(scce_to_epick((signed long long int)(1)) == true);
+#endif
+
+  // int* is not a fundamental type, so this goes through Enum_converter(bool)
+  int a = 123;
+  auto a_ptr = &a;
+  assert(sci_to_epick(a_ptr) == true);
+
+  // this does not compile because there is no conversion between Interval_nt and EPECK::FT
+//  assert(sci_to_epeck(2.) == EPECK::FT(2));
+
+  assert(epeck_to_epick(EPECK::FT(2)) == EPICK::FT(2));
+  assert(epeck_to_epick(2.) == EPICK::FT(2)); // double --> EPECK::FT --> EPICK::FT
+
+  assert(shi_to_shd(2.) == SHD::FT(2)); // double --> SHI::FT --> SHD::FT
+
+  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.) == SHD::FT(2)); // double --> SHE::RT --> SHD::FT
+
+  std::cout << "Done" << std::endl;
+
+  return EXIT_SUCCESS;
+}