diff --git a/Envelope_2/doc/Envelope_2/CGAL/envelope_2.h b/Envelope_2/doc/Envelope_2/CGAL/envelope_2.h
index 5dd0d75a15f..b2a761b1dc9 100644
--- a/Envelope_2/doc/Envelope_2/CGAL/envelope_2.h
+++ b/Envelope_2/doc/Envelope_2/CGAL/envelope_2.h
@@ -40,6 +40,28 @@ namespace CGAL {
 /*!
 \ingroup PkgEnvelope2Ref
 
+Computes the lower envelope of a set of \f$ x\f$-monotone curves in
+\f$ \mathbb{R}^2\f$, as given by the range `[begin, end)` with the help
+of the arrangement traits object `traits` responsible for their creation.
+Reusing the same traits object improves speed if the traits class caches data.
+The lower envelope is represented using the output minimization diagram `diag`.
+
+\tparam InputIterator must be an input iterator with value type `EnvelopeDiagram::X_monotone_curve_2`.
+\tparam Traits must be a model of the concept `ArrangementXMonotoneTraits_2`.
+\tparam EnvelopeDiagram must be a model of the concept `EnvelopeDiagram_1`.
+*/
+template<class InputIterator, class Traits, class EnvelopeDiagram>
+void lower_envelope_x_monotone_2
+(InputIterator begin, InputIterator end,
+const Traits* traits, EnvelopeDiagram& diag);
+
+} /* namespace CGAL */
+
+namespace CGAL {
+
+/*!
+\ingroup PkgEnvelope2Ref
+
 Computes the upper envelope of a set of curves in \f$ \mathbb{R}^2\f$,
 as given by the range `[begin, end)`. The upper envelope is
 represented using the output maximization diagram `diag`.
@@ -71,3 +93,25 @@ void upper_envelope_x_monotone_2
 EnvelopeDiagram& diag);
 
 } /* namespace CGAL */
+
+namespace CGAL {
+
+/*!
+\ingroup PkgEnvelope2Ref
+
+Computes the upper envelope of a set of \f$ x\f$-monotone curves in
+\f$ \mathbb{R}^2\f$, as given by the range `[begin, end)` with the help
+of the arrangement traits object `traits` responsbile for their creation.
+Reusing the same traits object improves speed if the traits class caches data.
+The upper envelope is represented using the output maximization diagram `diag`.
+
+\tparam InputIterator must be an input iterator with value type `EnvelopeDiagram::X_monotone_curve_2`.
+\tparam Traits must be a model of the concept `ArrangementXMonotoneTraits_2`.
+\tparam EnvelopeDiagram must be a model of the concept `EnvelopeDiagram_1`.
+*/
+template<class InputIterator, class Traits, class EnvelopeDiagram>
+void upper_envelope_x_monotone_2
+(InputIterator begin, InputIterator end,
+const Traits* traits, EnvelopeDiagram& diag);
+
+} /* namespace CGAL */
diff --git a/Envelope_2/include/CGAL/envelope_2.h b/Envelope_2/include/CGAL/envelope_2.h
index 2f1277e4c18..09db9e88e51 100644
--- a/Envelope_2/include/CGAL/envelope_2.h
+++ b/Envelope_2/include/CGAL/envelope_2.h
@@ -101,7 +101,7 @@ void lower_envelope_x_monotone_2 (InputIterator begin, InputIterator end,
  * \param diag Output: The minimization diagram.
  * \pre The value-type of the iterator is Traits::X_monotone_curve_2.
  */
-template <class InputIterator, class EnvelopeDiagram, class Traits>
+template <class InputIterator, class Traits, class EnvelopeDiagram>
 void lower_envelope_x_monotone_2 (InputIterator begin, InputIterator end,
                                   const Traits* traits, EnvelopeDiagram& diag)
 {
@@ -148,7 +148,7 @@ void upper_envelope_x_monotone_2 (InputIterator begin, InputIterator end,
  * \param diag Output: The maximization diagram.
  * \pre The value-type of the iterator is Traits::X_monotone_curve_2.
  */
-template <class InputIterator, class EnvelopeDiagram, class Traits>
+template <class InputIterator, class Traits, class EnvelopeDiagram>
 void upper_envelope_x_monotone_2 (InputIterator begin, InputIterator end,
                                   const Traits* traits, EnvelopeDiagram& diag)
 {