diff --git a/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_2.h b/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_2.h
index 26f6eb80270..6b1524e117e 100644
--- a/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_2.h
+++ b/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_2.h
@@ -46,9 +46,12 @@ There are three versions of constrained triangulations
 <LI>In the basic version, the constrained triangulation 
 does not handle intersecting constraints, and the set of input 
 constraints is required to be a set of polylines that do not intersect 
-except possibly at their endpoints. Any number of constrained edges 
-may share the same endpoint. Constrained edges may be vertical or
-have zero length. 
+except possibly at their endpoints.
+An exception of type `Intersection_of_constraints_exception`
+is thrown upon insertion of a constraint intersecting in
+its interior an already inserted constraint.
+Any number of constrained edges may share the same endpoint.
+Constrained edges may be vertical or have zero length.
 <LI>The two other versions support intersecting input constraints. 
 In those versions, input constraints may consist of 
 intersecting, overlapping or partially 
@@ -329,7 +332,9 @@ Note that `t` is first cleared.
 */ 
 istream& operator>>(istream& is,Constrained_triangulation_2<Traits,Tds> Ct& t); 
 
-//! Exception thrown for `intersect()` when called with the tag `No_intersection_tag`.
-//! Then, if constraints intersect, an exception of this type will be thrown.
+/*! Exception used by constrained triangulations configured with
+the tag `No_intersection_tag`. It is thrown upon insertion of a constraint
+that is intersecting an already inserted constraint in its interior.
+*/
 class Intersection_of_constraints_exception;
 } /* end namespace CGAL */
diff --git a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
index 0355f1976c3..a7cb8b2cc69 100644
--- a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
@@ -888,14 +888,14 @@ intersect(Face_handle f, int i,
 // split constraint edge (f,i) 
 // and return the Vertex_handle of the new Vertex
 { 
-#ifndef CGAL_NO_WARNING_WHEN_USING_CDT_PLUS_WHILE_INTERSECTING_CONSTRAINTS
+#ifndef CGAL_NO_CDT_2_WARNING
   CGAL_warning_msg(false,
-  "You are using an exact number type\n"
+  "You are using an exact number type,\n"
   "using a Constrained_triangulation_plus_2 class\n"
   "would avoid cascading intersection computation\n"
   " and be much more efficient\n"
-  "This message is shown only when not using "
-  "CGAL_NO_WARNING_WHEN_USING_CDT_PLUS_WHILE_INTERSECTING_CONSTRAINTS.\n");
+  "This message is shown only if CGAL_NO_CDT_2_WARNING"
+  "is not defined.\n");
 #endif
   const Point& pa = vaa->point();
   const Point& pb = vbb->point();