diff --git a/Packages/Min_sphere_of_spheres_d/include/CGAL/Min_sphere_of_spheres_d.C b/Packages/Min_sphere_of_spheres_d/include/CGAL/Min_sphere_of_spheres_d.C
index 4c90e40f3f3..91e70e91ecb 100644
--- a/Packages/Min_sphere_of_spheres_d/include/CGAL/Min_sphere_of_spheres_d.C
+++ b/Packages/Min_sphere_of_spheres_d/include/CGAL/Min_sphere_of_spheres_d.C
@@ -83,8 +83,7 @@ namespace CGAL_MINIBALL_NAMESPACE {
   
       for (i=e; i<n; ++i)
         if (!ss.contains(t.center_cartesian_begin(l[i]),
-                         t.radius(l[i]),Tol,Is_exact())) {
-          pivot(i);
+                         t.radius(l[i]),Tol,Is_exact()) && pivot(i)) {
           k = i+1;
           break;
         }
diff --git a/Packages/Min_sphere_of_spheres_d/web/Min_sphere_of_spheres_d.fw b/Packages/Min_sphere_of_spheres_d/web/Min_sphere_of_spheres_d.fw
index 5a3873b9e1d..6977b0dec98 100644
--- a/Packages/Min_sphere_of_spheres_d/web/Min_sphere_of_spheres_d.fw
+++ b/Packages/Min_sphere_of_spheres_d/web/Min_sphere_of_spheres_d.fw
@@ -3064,8 +3064,7 @@ void Min_sphere_of_spheres_d<Traits>::update(LP_algorithm) {
 
     for (i=e; i<n; ++i)
       if (!ss.contains(t.center_cartesian_begin(l[i]),
-                       t.radius(l[i]),Tol,Is_exact())) {
-        pivot(i);
+                       t.radius(l[i]),Tol,Is_exact()) && pivot(i)) {
         k = i+1;
         break;
       }
@@ -3075,8 +3074,9 @@ void Min_sphere_of_spheres_d<Traits>::update(LP_algorithm) {
 %
 This works fine in theory.  However, for approximate computation our
 implementation of \code{pivot()} might fail under certain
-circumstances, so termination is not guaranteed.  That's why this
-algorithm is not the default algorithm.
+circumstances.  In such a case we proceed as if the violating ball
+were contained in the current ball.  In this way, termination is
+guaranteed.
 %
 \subsection{The implementation of the farthest-first heuristic}
 %