diff --git a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_compare_at_x b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_compare_at_x
index 281059c478c..2ee70ee5dec 100644
--- a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_compare_at_x
+++ b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_compare_at_x
@@ -9,7 +9,8 @@ s -1 3 3 -1
 e 3 2  0 0  -3 0  3 0
 # Curve #2: part of the upper portion of the right branch of the hyperbola
 #           (x/2)^2 - (y/1)^2 = 1
-h 2 1  0 0  3 1.118034  2 0
+#           given by its intersections with x=2 and x=3.
+i 1 -4 0 0 0 -4   3 1.118034  0 0 0 1 0  -3   2 0  0 0 0 1 0  -2
 # Curve #3: the upper part of the circle x^2 + y^2 = 2^2.
 e 2 2  0 0  -2 0  2 0
 # Curve #4: the lower part of the circle x^2 + (y-3)^2 = 1^2
diff --git a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_between_cw b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_between_cw
index 80da0e9c532..a6f1fe79ccf 100644
--- a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_between_cw
+++ b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_between_cw
@@ -17,8 +17,8 @@ s 0 0  0 -3
 e 3 1  0 -1  -3 -1  0 0
 # Curve #6: a horizontal segment
 s -2 0  0 0
-# curve #7: a portion of the hyperbola y + 1 = 1/(x + 1)
-a 0 0 1 1 1 0  -0.9 9  0 0
+# curve #7: a segment
+s -1 1  0 0
 #-----------------------------------------------------------
 # Number of "stand alone" points
 1
diff --git a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_between_cw_full b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_between_cw_full
index 5dfbbce6166..f76ba0a4a12 100644
--- a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_between_cw_full
+++ b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_between_cw_full
@@ -17,8 +17,8 @@ s 0 0  0 -3
 e 3 1  0 -1  -3 -1  0 0
 # Curve #6: a horizontal segment
 s -2 0  0 0
-# curve #7: a portion of the hyperbola y + 1 = 1/(x + 1)
-a 0 0 1 1 1 0  -0.9 9  0 0
+# curve #7: a segment
+s -1 1  0 0
 #-----------------------------------------------------------
 # Number of "stand alone" points
 1
diff --git a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_in_x_range b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_in_x_range
index b6d3869922a..9a15d599ef0 100644
--- a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_in_x_range
+++ b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_is_in_x_range
@@ -9,8 +9,9 @@ e 5 3  0 0  0 3  5 0
 s -1 3  2 4
 # Curve #2: a vertical segment
 s 0 1  0 0
-# Curve #3: a portion of the hyperbola y = 1/x
-a 0 0 1 0 0 -1  0.1 10  2 0.5
+# Curve #3: a portion of the upper branch of the hyperbola y = 1/x
+#           given by its intersections with y=100x and x=4y
+i 0 0 1 0 0 -1   0.1 10  0 0 0 100 -1 0   2 0.5  0 0 0 1 -4 0
 # Curve #4: a portion of the parabola y = 3*x^2 - 2*x + 5
 a 3 0 0 -2 -1 5  2 13  -1 10
 #-----------------------------------------------------------
diff --git a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_split b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_split
index 473fb38c530..26588ccbacd 100644
--- a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_split
+++ b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_curve_split
@@ -8,8 +8,9 @@ e 5 3  0 0  -5 0  5 0
 s -1 3  3 -1
 # Curve #2: a vertical segment
 s 0 -2  0 0
-# Curve #3: a portion of the hyperbola y = 1/x
-a 0 0 1 0 0 -1  0.1 10  2 0.5
+# Curve #3: a portion of the upper branch of the hyperbola y = 1/x
+#           given by its intersections with y=100x and x=4y
+i 0 0 1 0 0 -1   0.1 10  0 0 0 100 -1 0   2 0.5  0 0 0 1 -4 0
 # Curve #4: a portion of the parabola y = 3*x^2 - 2*x + 5
 a 3 0 0 -2 -1 5  2 13  -1 10
 #-----------------------------------------------------------
diff --git a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_get_point_status b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_get_point_status
index 9d698ff1aee..9f6cac7bed5 100644
--- a/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_get_point_status
+++ b/Packages/Arrangement/test/Arrangement_2_Traits/DATA/conic_arcs/conic_get_point_status
@@ -8,8 +8,9 @@ e 5 3  0 0  -5 0  5 0
 s -1 3  3 -1
 # Curve #2: a vertical segment
 s 0 -2  0 0
-# Curve #3: a portion of the hyperbola y = 1/x
-a 0 0 1 0 0 -1  0.1 10  2 0.5
+# Curve #3: a portion of the upper branch of the hyperbola y = 1/x
+#           given by its intersections with y=100x and x=4y
+i 0 0 1 0 0 -1   0.1 10  0 0 0 100 -1 0   2 0.5  0 0 0 1 -4 0
 # Curve #4: a portion of the parabola y = 3*x^2 - 2*x + 5
 a 3 0 0 -2 -1 5  2 13  -1 10
 #-----------------------------------------------------------
diff --git a/Packages/Arrangement/test/Arrangement_2_Traits/include/Conic_traits_test.h b/Packages/Arrangement/test/Arrangement_2_Traits/include/Conic_traits_test.h
index 834d1f4aa4e..f4af85143b5 100644
--- a/Packages/Arrangement/test/Arrangement_2_Traits/include/Conic_traits_test.h
+++ b/Packages/Arrangement/test/Arrangement_2_Traits/include/Conic_traits_test.h
@@ -14,9 +14,10 @@ public Base_traits_test<Traits_class, Number_type>
   typedef Number_type  NT;
 
   typedef typename Traits_class::Point_2        Point;
+  typedef typename Traits_class::Segment_2      Segment;
+  typedef typename Traits_class::Circle_2       Circle;
   typedef typename Traits_class::X_curve_2      X_curve;
   typedef typename Traits_class::Curve_2        Curve;
-  typedef typename Traits_class::Curve_2        Conic;
 
  public:
   
@@ -50,12 +51,13 @@ read_curve (std::ifstream & is, Curve & cv)
   char one_line[128];
 
   skip_comments (is, one_line);
-  std::string stringvalues(one_line);
-  std::istringstream str_line (stringvalues, std::istringstream::in);
+  std::istrstream str_line( one_line, 128 );
 
   // Get the arc type.
-  char  type;
-  Conic conic;
+  char     type;
+  bool     is_circle = false;              // Is this a circle.
+  Circle   circle;
+  NT       r, s, t, u, v, w;               // The conic coefficients.
 
   str_line >> type;
 
@@ -75,14 +77,29 @@ read_curve (std::ifstream & is, Curve & cv)
     NT     a_sq = a*a;
     NT     b_sq = b*b;
 
-    conic = Conic (b_sq, a_sq, 0,
-		   -2*x0*b_sq, -2*y0*a_sq,
-		   x0*x0*b_sq + y0*y0*a_sq - a_sq*b_sq);
+    if (a == b)
+    {
+      is_circle = true;
+      circle = Circle (Point (x0, y0), a*b, CGAL::CLOCKWISE);
+    }
+    else
+    {
+      r = b_sq;
+      s = a_sq;
+      t = 0;
+      u = -2*x0*b_sq;
+      v = -2*y0*a_sq;
+      w = x0*x0*b_sq + y0*y0*a_sq - a_sq*b_sq;
+    }
 
     if (type == 'f' || type == 'F')
     {
-      // Create a full ellipse.
-      cv = Curve(conic);
+      // Create a full ellipse (or circle).
+      if (is_circle)
+	cv = Curve (circle);
+      else
+	cv = Curve (r, s, t, u, v, w);
+
       return;
     }
   }
@@ -101,9 +118,12 @@ read_curve (std::ifstream & is, Curve & cv)
     NT     a_sq = a*a;
     NT     b_sq = b*b;
 
-    conic = Conic (b_sq, -a_sq, 0,
-		   -2*x0*b_sq, 2*y0*a_sq,
-		   x0*x0*b_sq - y0*y0*a_sq - a_sq*b_sq);  
+    r = b_sq;
+    s= -a_sq;
+    t = 0;
+    u = -2*x0*b_sq;
+    v = 2*y0*a_sq;
+    w = x0*x0*b_sq - y0*y0*a_sq - a_sq*b_sq;  
   }
   else if (type == 'p' || type == 'P')
   {
@@ -116,23 +136,22 @@ read_curve (std::ifstream & is, Curve & cv)
     
     str_line >> c >> x0 >> y0;
     
-    conic = Conic (1, 0, 0,
-		   -2*x0, -4*c,
-		   x0*x0 + 4*c*y0);
+    r = 1;
+    s = 0;
+    t = 0;
+    u = -2*x0;
+    v = -4*c;
+    w = x0*x0 + 4*c*y0;
   }
   else if (type == 'c' || type == 'C' || type == 'a' || type == 'A')
   {
     // Read a general conic, given by its coefficients <r,s,t,u,v,w>.
-    NT      r, s, t, u, v, w;
-
     str_line >> r >> s >> t >> u >> v >> w;
 
-    conic = Conic (r, s, t, u, v, w);
-
     if (type == 'c' || type == 'C')
     {
       // Create a full conic (should work only for ellipses).
-      cv = Curve(conic);
+      cv = Curve (r, s, t, u, v, w);
       return;
     }
   }
@@ -143,18 +162,51 @@ read_curve (std::ifstream & is, Curve & cv)
 
     str_line >> x1 >> y1 >> x2 >> y2;
 
-    conic = Conic (0, 0, 0,
-		   y1 - y2, x2 - x1,
-		   x1*y2 - x2*y1);
+    Point   source (x1, y1);
+    Point   target (x2, y2);
+    Segment segment (source, target);
 
     // Create the segment.
-    cv = Curve(conic, Point(x1,y1), Point(x2,y2));
+    cv = Curve (segment);
     return;
   }
+  else if (type == 'i' || type == 'I')
+  {
+    // Read a general conic, given by its coefficients <r,s,t,u,v,w>.
+    str_line >> r >> s >> t >> u >> v >> w;
 
+    // Read the approximated source, along with a general conic 
+    // <r_1,s_1,t_1,u_1,v_1,w_1> whose intersection with <r,s,t,u,v,w>
+    // defines the source.
+    NT     r1, s1, t1, u1, v1, w1;
+    NT     x1, y1;
+
+    str_line >> x1 >> y1;
+    str_line >> r1 >> s1 >> t1 >> u1 >> v1 >> w1;
+
+    Point   app_source (x1, y1);
+
+    // Read the approximated target, along with a general conic 
+    // <r_2,s_2,t_2,u_2,v_2,w_2> whose intersection with <r,s,t,u,v,w>
+    // defines the target.
+    NT     r2, s2, t2, u2, v2, w2;
+    NT     x2, y2;
+
+    str_line >> x2 >> y2;
+    str_line >> r2 >> s2 >> t2 >> u2 >> v2 >> w2;
+
+    Point   app_target (x2, y2);
+
+    // Create the conic arc.
+    cv = Curve (r, s, t, u, v ,w,
+		app_source, r1, s1, t1, u1, v1, w1,
+		app_target, r2, s2, t2, u2, v2, w2);
+    return;
+  }
   else
   {
-    std::cerr << "Illegal conic type specification: " << type << "." << std::endl;
+    std::cerr << "Illegal conic type specification: " << type << "."
+              << std::endl;
     return;
   }
 
@@ -166,10 +218,17 @@ read_curve (std::ifstream & is, Curve & cv)
   Point source (x1, y1);
   Point target (x2, y2);
 
-  // Create the circular arc.
-  cv = Curve (conic, 
-	      source, target,
-	      _error_eps);           // It's OK to move the endpoints a bit.
+  // Create the conic (or circular) arc.
+  if (is_circle)
+  {
+    cv = Curve (circle,
+		  source, target);
+  }
+  else
+  {
+    cv = Curve (r, s, t, u, v, w,
+		  source, target);
+  }
  
   return;
 }