diff --git a/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/global_functions.tex b/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/global_functions.tex
index e9d41740222..8376c0c614b 100644
--- a/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/global_functions.tex
+++ b/Circular_kernel_3/doc_tex/Circular_kernel_3_ref/global_functions.tex
@@ -4,8 +4,9 @@
 
 \ccFunction{Circular_arc_point_3<SphericalKernel>
   x_extremal_point(Const Sphere_3<SphericalKernel> & c, bool b);}
-{Returns the point on the sphere that is the smallest (resp. largest)
-  point in the $x$-direction if $b$ is \ccc{true}
+{Returns the point on the sphere that is extremal in the
+  $x$-direction, and that is the smallest (resp. largest) of the two
+  $x$-extremal points for the lexicographic order if $b$ is \ccc{true} 
   (resp. \ccc{false}).}
 
 \ccFunction{Circular_arc_point_3<SphericalKernel>
@@ -19,8 +20,9 @@
 
 \ccFunction{Circular_arc_point_3<SphericalKernel>
   y_extremal_point(const Sphere_3<SphericalKernel> & c, bool b);}
-{Returns the point on the sphere that is the smallest (resp. largest)
-  point in the $y$-direction if $b$ is \ccc{true}
+{Returns the point on the sphere that is extremal in the
+  $y$-direction, and that is the smallest (resp. largest) of the two
+  $y$-extremal points for the lexicographic order if $b$ is \ccc{true} 
   (resp. \ccc{false}).}
 
 \ccFunction{Circular_arc_point_3<SphericalKernel>
@@ -34,8 +36,9 @@
 
 \ccFunction{Circular_arc_point_3<SphericalKernel>
   z_extremal_point(const Sphere_3<SphericalKernel> & c, bool b);}
-{Returns the point on the sphere that is the smallest (resp. largest)
-  point in the $z$-direction if $b$ is \ccc{true}
+{Returns the point on the sphere that is extremal in the
+  $z$-direction, and that is the smallest (resp. largest) of the two
+  $z$-extremal points for the lexicographic order if $b$ is \ccc{true} 
   (resp. \ccc{false}).}
 
 \ccFunction{Circular_arc_point_3<SphericalKernel>