diff --git a/Cartesian_kernel/include/CGAL/Cartesian_converter.h b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
index 89595b5ef34..576c6e78599 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian_converter.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian_converter.h
@@ -127,14 +127,20 @@ public:
     }
 
     template <typename T>
-    typename K2::FT
-    operator()(const T&,
+    T
+    operator()(const T t,
                typename std::enable_if<std::is_fundamental<T>::value>::type* = nullptr) const
     {
-        // Disable fundamental types (other than K1::FT) to avoid unexpected results
-        // More details: https://github.com/CGAL/cgal/issues/4982
-        CGAL_static_assertion(!(std::is_fundamental<T>::value));
-        return typename K2::FT();
+        return t;
+    }
+
+    template <typename T>
+    T
+    operator()(const T t,
+               typename std::enable_if<!std::is_fundamental<T>::value>::type* = nullptr) const
+    {
+        CGAL_static_assertion(!(std::is_same<T, T>::value));
+        return t;
     }
 
     // drop the boost::detail::variant::void_ generated by the macros
diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h b/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
index b8cc0939f1b..cb22a9548b9 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous_converter.h
@@ -87,14 +87,20 @@ public:
     }
 
     template <typename T>
-    typename K2::FT
-    operator()(const T&,
-               typename std::enable_if<std::is_fundamental<T>::value>::type* = nullptr)
+    T
+    operator()(const T t,
+               typename std::enable_if<std::is_fundamental<T>::value>::type* = nullptr) const
     {
-        // Disable fundamental types (other than K1::FT) to avoid unexpected results
-        // More details: https://github.com/CGAL/cgal/issues/4982
-        CGAL_static_assertion(!(std::is_fundamental<T>::value));
-        return typename K2::FT();
+        return t;
+    }
+
+    template <typename T>
+    T
+    operator()(const T t,
+               typename std::enable_if<!std::is_fundamental<T>::value>::type* = nullptr) const
+    {
+        CGAL_static_assertion(!(std::is_same<T, T>::value));
+        return t;
     }
 
     typename K2::Point_2
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 cb801622c9f..c207c83dee7 100644
--- a/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h
+++ b/Kernel_d/include/CGAL/Kernel_d/Cartesian_converter_d.h
@@ -100,14 +100,20 @@ public:
     }
 
     template <typename T>
-    typename K2::FT
-    operator()(const T&,
+    T
+    operator()(const T t,
                typename std::enable_if<std::is_fundamental<T>::value>::type* = nullptr) const
     {
-        // Disable fundamental types (other than K1::FT) to avoid unexpected results
-        // More details: https://github.com/CGAL/cgal/issues/4982
-        CGAL_static_assertion(!(std::is_fundamental<T>::value));
-        return typename K2::FT();
+        return t;
+    }
+
+    template <typename T>
+    T
+    operator()(const T t,
+               typename std::enable_if<!std::is_fundamental<T>::value>::type* = nullptr) const
+    {
+        CGAL_static_assertion(!(std::is_same<T, T>::value));
+        return t;
     }
 
     std::vector<Object>
@@ -121,11 +127,6 @@ public:
       return res;
     }
 
-    int operator()(const int &a)
-    {
-        return a;
-    }
-
     typename K2::Point_d
     operator()(const typename K1::Point_d &a) const
     {