diff --git a/Packages/Triangulation_3/changes.txt b/Packages/Triangulation_3/changes.txt
index a798de54ae6..83af97b3a03 100644
--- a/Packages/Triangulation_3/changes.txt
+++ b/Packages/Triangulation_3/changes.txt
@@ -1,5 +1,6 @@
 Version 1.105 (?? February 02)
 - Shorten DS_Container::Free_elt so that TDS_2 can use it.
+- New insert(Point, Locate_type, Cell_handle, int, int).
 
 Version 1.104 (5 February 02)
 - Various internal cleanups.
diff --git a/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Delaunay_triangulation_3.tex b/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Delaunay_triangulation_3.tex
index 147d99bcad8..0e7d2684f88 100644
--- a/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Delaunay_triangulation_3.tex
+++ b/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Delaunay_triangulation_3.tex
@@ -81,6 +81,13 @@ triangulations.
 addition the empty sphere property of all the created faces.
 The optional argument \ccc{start} is used as a starting place for the search.}
 
+\ccMethod{Vertex_handle insert(const Point & p, Locate_type lt,
+                               Cell_handle loc, int li, int lj);}
+{Inserts point \ccc{p} in the triangulation and returns the corresponding
+ vertex. Similar to the above \ccc{insert()} function, but takes as additional
+ parameter the return values of a previous location query.  See description of
+ \ccc{locate()} above.}
+
 The following method allows one to insert several points. It returns the
 number of inserted points. 
 
@@ -91,21 +98,6 @@ number of inserted points.
 \ccc{last}$\left.\right)$. 
 \ccPrecond{The \ccc{value_type} of \ccc{first} and \ccc{last} is
 \ccc{Point}.}}
-%\ccMethod{int insert(list<Point>::const_iterator first,
-%	     list<Point>::const_iterator last);}
-%{}
-%\ccGlue
-%\ccMethod{int insert(vector<Point>::const_iterator first,
-%	     vector<Point>::const_iterator last);}
-%{}
-%\ccGlue
-%\ccMethod{int insert(istream_iterator<Point, ptrdiff_t> first,
-%	     istream_iterator<Point, ptrdiff_t> last);}
-%{}
-%\ccGlue
-%\ccMethod{int insert(Point* first,
-%	     Point* last);}
-%{}
 
 \ccHeading{Removal}
 
diff --git a/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Regular_triangulation_3.tex b/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Regular_triangulation_3.tex
index 130edaa3f59..6b63cd44b4b 100644
--- a/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Regular_triangulation_3.tex
+++ b/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Regular_triangulation_3.tex
@@ -90,6 +90,13 @@ insertion creates a vertex, this vertex is returned. Otherwise, this
 method returns \ccc{NULL}.
 The optional argument \ccc{start} is used as a starting place for the search.}
 
+\ccMethod{Vertex_handle insert(const Weighted_point & p, Locate_type lt,
+                               Cell_handle loc, int li, int lj);}
+{Inserts point \ccc{p} in the triangulation and returns the corresponding
+ vertex. Similar to the above \ccc{insert()} function, but takes as additional
+ parameter the return values of a previous location query.  See description of
+ \ccc{locate()} above.}
+
 The following method allows one to insert several points. It returns the
 number of inserted points. 
 
diff --git a/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Triangulation_3.tex b/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Triangulation_3.tex
index 0ce2e582d2d..ba80d70a15e 100644
--- a/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Triangulation_3.tex
+++ b/Packages/Triangulation_3/doc_tex/Triangulation_3_ref/Triangulation_3.tex
@@ -564,6 +564,13 @@ triangulate the new infinite face. See
 Figure~\ref{Triangulation3-fig-insert_outside_affine_hull}.
 The optional argument \ccc{start} is used as a starting place for the search.}
 
+\ccMethod{Vertex_handle insert(const Point & p, Locate_type lt,
+                               Cell_handle loc, int li, int lj);}
+{Inserts point \ccc{p} in the triangulation and returns the corresponding
+ vertex. Similar to the above \ccc{insert()} function, but takes as additional
+ parameter the return values of a previous location query.  See description of
+ \ccc{locate()} above.}
+
 \ccMethod{template < class InputIterator >
           int
           insert(InputIterator first, InputIterator last);}
diff --git a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Delaunay_triangulation_3.tex b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Delaunay_triangulation_3.tex
index 147d99bcad8..0e7d2684f88 100644
--- a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Delaunay_triangulation_3.tex
+++ b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Delaunay_triangulation_3.tex
@@ -81,6 +81,13 @@ triangulations.
 addition the empty sphere property of all the created faces.
 The optional argument \ccc{start} is used as a starting place for the search.}
 
+\ccMethod{Vertex_handle insert(const Point & p, Locate_type lt,
+                               Cell_handle loc, int li, int lj);}
+{Inserts point \ccc{p} in the triangulation and returns the corresponding
+ vertex. Similar to the above \ccc{insert()} function, but takes as additional
+ parameter the return values of a previous location query.  See description of
+ \ccc{locate()} above.}
+
 The following method allows one to insert several points. It returns the
 number of inserted points. 
 
@@ -91,21 +98,6 @@ number of inserted points.
 \ccc{last}$\left.\right)$. 
 \ccPrecond{The \ccc{value_type} of \ccc{first} and \ccc{last} is
 \ccc{Point}.}}
-%\ccMethod{int insert(list<Point>::const_iterator first,
-%	     list<Point>::const_iterator last);}
-%{}
-%\ccGlue
-%\ccMethod{int insert(vector<Point>::const_iterator first,
-%	     vector<Point>::const_iterator last);}
-%{}
-%\ccGlue
-%\ccMethod{int insert(istream_iterator<Point, ptrdiff_t> first,
-%	     istream_iterator<Point, ptrdiff_t> last);}
-%{}
-%\ccGlue
-%\ccMethod{int insert(Point* first,
-%	     Point* last);}
-%{}
 
 \ccHeading{Removal}
 
diff --git a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Regular_triangulation_3.tex b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Regular_triangulation_3.tex
index 130edaa3f59..6b63cd44b4b 100644
--- a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Regular_triangulation_3.tex
+++ b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Regular_triangulation_3.tex
@@ -90,6 +90,13 @@ insertion creates a vertex, this vertex is returned. Otherwise, this
 method returns \ccc{NULL}.
 The optional argument \ccc{start} is used as a starting place for the search.}
 
+\ccMethod{Vertex_handle insert(const Weighted_point & p, Locate_type lt,
+                               Cell_handle loc, int li, int lj);}
+{Inserts point \ccc{p} in the triangulation and returns the corresponding
+ vertex. Similar to the above \ccc{insert()} function, but takes as additional
+ parameter the return values of a previous location query.  See description of
+ \ccc{locate()} above.}
+
 The following method allows one to insert several points. It returns the
 number of inserted points. 
 
diff --git a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Triangulation_3.tex b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Triangulation_3.tex
index 0ce2e582d2d..ba80d70a15e 100644
--- a/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Triangulation_3.tex
+++ b/Packages/Triangulation_3/doc_tex/basic/Triangulation_3_ref/Triangulation_3.tex
@@ -564,6 +564,13 @@ triangulate the new infinite face. See
 Figure~\ref{Triangulation3-fig-insert_outside_affine_hull}.
 The optional argument \ccc{start} is used as a starting place for the search.}
 
+\ccMethod{Vertex_handle insert(const Point & p, Locate_type lt,
+                               Cell_handle loc, int li, int lj);}
+{Inserts point \ccc{p} in the triangulation and returns the corresponding
+ vertex. Similar to the above \ccc{insert()} function, but takes as additional
+ parameter the return values of a previous location query.  See description of
+ \ccc{locate()} above.}
+
 \ccMethod{template < class InputIterator >
           int
           insert(InputIterator first, InputIterator last);}
diff --git a/Packages/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h b/Packages/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h
index 178b85719f2..79def31e677 100644
--- a/Packages/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h
+++ b/Packages/Triangulation_3/include/CGAL/Delaunay_triangulation_3.h
@@ -201,6 +201,9 @@ public:
 
   Vertex_handle insert(const Point & p, Cell_handle start = NULL);
 
+  Vertex_handle insert(const Point & p, Locate_type lt,
+	               Cell_handle c, int li, int);
+ 
   // Obsolete.
   Vertex_handle push_back(const Point & p)
   {
@@ -372,13 +375,21 @@ template < class Gt, class Tds >
 typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
 Delaunay_triangulation_3<Gt,Tds>::
 insert(const Point & p, Cell_handle start)
+{
+    Locate_type lt;
+    int li, lj;
+    Cell_handle c = locate(p, lt, li, lj, start);
+    return insert(p, lt, c, li, lj);
+}
+
+template < class Gt, class Tds >
+typename Delaunay_triangulation_3<Gt,Tds>::Vertex_handle
+Delaunay_triangulation_3<Gt,Tds>::
+insert(const Point & p, Locate_type lt, Cell_handle c, int li, int)
 {
   switch (dimension()) {
   case 3:
     {
-      Locate_type lt;
-      int li, lj;
-      Cell_handle c = locate( p, lt, li, lj, start);
       if ( lt == VERTEX )
 	  return c->vertex(li);
 
@@ -389,9 +400,6 @@ insert(const Point & p, Cell_handle start)
     }// dim 3
   case 2:
     {
-      Locate_type lt;
-      int li, lj;
-      Cell_handle c = locate( p, lt, li, lj, start);
       switch (lt) {
       case OUTSIDE_CONVEX_HULL:
       case CELL:
@@ -413,9 +421,9 @@ insert(const Point & p, Cell_handle start)
     }//dim 2
   default :
     // dimension <= 1
-    return Tr_Base::insert(p,start);
+    return Tr_Base::insert(p, c);
   }
-}// insert(p)
+}
 
 template < class Gt, class Tds >
 void
diff --git a/Packages/Triangulation_3/include/CGAL/Regular_triangulation_3.h b/Packages/Triangulation_3/include/CGAL/Regular_triangulation_3.h
index 407e31eeb31..60acffe0e0b 100644
--- a/Packages/Triangulation_3/include/CGAL/Regular_triangulation_3.h
+++ b/Packages/Triangulation_3/include/CGAL/Regular_triangulation_3.h
@@ -95,7 +95,10 @@ public:
     return number_of_vertices() - n;
   }
 
-  Vertex_handle insert( const Weighted_point & p, Cell_handle start = NULL);
+  Vertex_handle insert(const Weighted_point & p, Cell_handle start = NULL);
+
+  Vertex_handle insert(const Weighted_point & p, Locate_type lt,
+	               Cell_handle c, int li, int);
 
   Vertex_handle push_back(const Weighted_point &p)
   {
@@ -353,14 +356,21 @@ template < class Gt, class Tds >
 typename Regular_triangulation_3<Gt,Tds>::Vertex_handle
 Regular_triangulation_3<Gt,Tds>::
 insert(const Weighted_point & p, Cell_handle start) 
+{
+    Locate_type lt;
+    int li, lj;
+    Cell_handle c = locate(p, lt, li, lj, start);
+    return insert(p, lt, c, li, lj);
+}
+
+template < class Gt, class Tds >
+typename Regular_triangulation_3<Gt,Tds>::Vertex_handle
+Regular_triangulation_3<Gt,Tds>::
+insert(const Weighted_point & p, Locate_type lt, Cell_handle c, int li, int)
 {
   switch (dimension()) {
   case 3: 
     {
-      Locate_type lt;
-      int li, lj;
-      Cell_handle c = locate( p, lt, li, lj, start);
-      
       if ( lt == VERTEX )
 	  return c->vertex(li);
       // choice: not to do anything
@@ -389,9 +399,6 @@ insert(const Weighted_point & p, Cell_handle start)
     }
   case 2:
     {
-      Locate_type lt;
-      int li, lj;
-      Cell_handle c = locate( p, lt, li, lj, start);
       switch (lt) {
       case OUTSIDE_CONVEX_HULL:
       case CELL:
@@ -429,9 +436,6 @@ insert(const Weighted_point & p, Cell_handle start)
     }//dim 2
   case 1:
     {
-      Locate_type lt;
-      int li, lj;
-      Cell_handle c = locate( p, lt, li, lj, start);
       switch (lt) {
       case OUTSIDE_CONVEX_HULL:
       case EDGE:
@@ -488,7 +492,7 @@ insert(const Weighted_point & p, Cell_handle start)
     }
   default :
     {
-      return Tr_Base::insert(p,start);
+      return Tr_Base::insert(p, c);
     }
   }
 }
diff --git a/Packages/Triangulation_3/include/CGAL/Triangulation_3.h b/Packages/Triangulation_3/include/CGAL/Triangulation_3.h
index deb914540e5..0418451b760 100644
--- a/Packages/Triangulation_3/include/CGAL/Triangulation_3.h
+++ b/Packages/Triangulation_3/include/CGAL/Triangulation_3.h
@@ -470,7 +470,9 @@ public:
   //INSERTION 
 
   Vertex_handle insert(const Point & p, Cell_handle start = NULL);
-
+  Vertex_handle insert(const Point & p, Locate_type lt, Cell_handle c,
+	               int li, int lj);
+ 
   // Obsolete.
   Vertex_handle push_back(const Point & p)
   {
@@ -2297,6 +2299,14 @@ insert(const Point & p, Cell_handle start)
   Locate_type lt;
   int li, lj;
   Cell_handle c = locate( p, lt, li, lj, start);
+  return insert(p, lt, c, li, lj);
+}
+
+template < class GT, class Tds >
+typename Triangulation_3<GT,Tds>::Vertex_handle
+Triangulation_3<GT,Tds>::
+insert(const Point & p, Locate_type lt, Cell_handle c, int li, int lj)
+{
   switch (lt) {
   case VERTEX:
     return c->vertex(li);
diff --git a/Packages/Triangulation_3/include/CGAL/Triangulation_hierarchy_3.h b/Packages/Triangulation_3/include/CGAL/Triangulation_hierarchy_3.h
index b360a3e0356..0dc830698d4 100644
--- a/Packages/Triangulation_3/include/CGAL/Triangulation_hierarchy_3.h
+++ b/Packages/Triangulation_3/include/CGAL/Triangulation_hierarchy_3.h
@@ -103,18 +103,25 @@ public:
   Cell_handle locate(const Point& p) const;
 
 private:
+
+  struct locs {
+      Cell_handle pos;
+      int li, lj;
+      Locate_type lt;
+  };
+
   void locate(const Point& p, Locate_type& lt, int& li, int& lj,
-	      Cell_handle pos[Triangulation_hierarchy_3__maxlevel]) const;
+	      locs pos[Triangulation_hierarchy_3__maxlevel]) const;
   int random_level();
 
   // added to make the test program of usual triangulations work
   // undocumented
 public:
 
-  // FIXME : This one could benefit from the hierarchy too.
-  Vertex_handle insert(const Point& p, Locate_type lt, Cell_handle loc, int li)
+  Vertex_handle insert(const Point& p, Locate_type lt, Cell_handle loc,
+	               int li, int lj)
   {
-    return Tr_Base::insert(p);
+    return Tr_Base::insert(p, lt, loc, li, lj);
   }
   
   Vertex_handle insert(const Point &p, Cell_handle start)
@@ -266,16 +273,27 @@ insert(const Point &p)
   Locate_type lt;
   int i, j;
   // locate using hierarchy
-  Cell_handle positions[Triangulation_hierarchy_3__maxlevel];
+  locs positions[Triangulation_hierarchy_3__maxlevel];
   locate(p, lt, i, j, positions);
   // insert at level 0
-  Vertex_handle vertex = hierarchy[0]->insert(p, positions[0]);
+  Vertex_handle vertex = hierarchy[0]->insert(p,
+	                                      positions[0].lt,
+	                                      positions[0].pos,
+	                                      positions[0].li,
+	                                      positions[0].lj);
   Vertex_handle previous = vertex;
   Vertex_handle first = vertex;
 
   int level = 1;
   while (level <= vertex_level ){
-    vertex = hierarchy[level]->insert(p, positions[level]);
+      if (positions[level].pos == NULL)
+          vertex = hierarchy[level]->insert(p);
+      else
+          vertex = hierarchy[level]->insert(p,
+	                                    positions[level].lt,
+	                                    positions[level].pos,
+	                                    positions[level].li,
+	                                    positions[level].lj);
     vertex->set_down((void *) &*previous);// link with level above
     previous->set_up((void *) &*vertex);
     previous=vertex;
@@ -310,9 +328,9 @@ typename Triangulation_hierarchy_3<Tr>::Cell_handle
 Triangulation_hierarchy_3<Tr>::
 locate(const Point& p, Locate_type& lt, int& li, int& lj) const
 {
-  Cell_handle positions[Triangulation_hierarchy_3__maxlevel];
+  locs positions[Triangulation_hierarchy_3__maxlevel];
   locate(p, lt, li, lj, positions);
-  return positions[0];
+  return positions[0].pos;
 }
 
 template <class Tr>
@@ -330,7 +348,7 @@ template <class Tr>
 void
 Triangulation_hierarchy_3<Tr>::
 locate(const Point& p, Locate_type& lt, int& li, int& lj,
-       Cell_handle pos[Triangulation_hierarchy_3__maxlevel]) const
+       locs pos[Triangulation_hierarchy_3__maxlevel]) const
 {
   int level = Triangulation_hierarchy_3__maxlevel;
 
@@ -342,13 +360,17 @@ locate(const Point& p, Locate_type& lt, int& li, int& lj,
   }
 
   for (int i=level+1; i<Triangulation_hierarchy_3__maxlevel; ++i)
-      pos[i]=0;
+      pos[i].pos=0;
 
   Cell_handle position(NULL);
   while(level > 0) {
     // locate at that level from "position"
     // result is stored in "position" for the next level
-    pos[level] = position = hierarchy[level]->locate(p, position);
+    pos[level].pos = position = hierarchy[level]->locate(p,
+	                                                 pos[level].lt,
+	                                                 pos[level].li,
+	                                                 pos[level].lj,
+	                                                 position);
     // find the nearest vertex.
     Vertex_handle nearest =
 	hierarchy[level]->nearest_vertex_in_cell(p, position);
@@ -358,7 +380,10 @@ locate(const Point& p, Locate_type& lt, int& li, int& lj,
     position = nearest->cell();                // incident cell
     --level;
   }
-  pos[0] = hierarchy[level]->locate(p, lt, li, lj, position);  // at level 0
+  pos[0].pos = hierarchy[level]->locate(p, lt, li, lj, position); // at level 0
+  pos[0].lt = lt;
+  pos[0].li = li;
+  pos[0].lj = lj;
 }