diff --git a/Envelope_2/doc_tex/Envelope_2_ref/Env_default_diagram.tex b/Envelope_2/doc_tex/Envelope_2_ref/Env_default_diagram.tex
index 308b7501ed7..35d419a6787 100644
--- a/Envelope_2/doc_tex/Envelope_2_ref/Env_default_diagram.tex
+++ b/Envelope_2/doc_tex/Envelope_2_ref/Env_default_diagram.tex
@@ -13,16 +13,18 @@
 \ccDefinition
 %============
 
-The default envelope-diagram class used by the envelops functions to represent
-the lower or the upper envelope of a set of curves. It is parameterized by a
-traits class, which is a model of the \ccc{ArrangementXMonotoneTraits_2}
-concept, in case we handle only envelopes of $x$-monotone curves, or of the
-refined \ccc{ArrangementTraits_2} concept in case we handle arbitrary planar
-curves.
+This class is the default envelope-diagram class used by envelope functions
+to represent the minimization or the maximization diagram of a set of curves. 
+It represents the diagram as a doubly-linked list of interleaved vertices
+and edges. Thus, all operations provided by the envelope diagram take constant
+time, and the space needed to store the diagram class is linear in the
+complexity of the envelope.
+
+The envelope-diagram class is parameterized by a traits class, which is a
+model of the \ccc{ArrangementXMonotoneTraits_2} concept, in case we handle
+only envelopes of $x$-monotone curves, or of the refined
+\ccc{ArrangementTraits_2} concept in case we handle arbitrary planar curves.
 
-The space needed by this envelope-diagram class is linear in the size of
-the minimization diagram, and traversing requires linear time.
- 
 \ccInclude{CGAL/Env_default_diagram_1.h}
 
 \ccIsModel