diff --git a/Packages/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h b/Packages/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h
index 10364505273..290b357af6f 100644
--- a/Packages/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h
+++ b/Packages/Cartesian_kernel/include/CGAL/Cartesian/Point_2.h
@@ -156,9 +156,9 @@ CGAL_KERNEL_INLINE
 Bbox_2
 PointC2<R>::bbox() const
 {
-  double bx = CGAL::to_double(x());
-  double by = CGAL::to_double(y());
-  return Bbox_2(bx,by, bx,by);
+  std::pair<double,double> xp = CGAL::to_interval(x());
+  std::pair<double,double> yp = CGAL::to_interval(y());
+  return Bbox_2(xp.first, yp.first,  xp.second, yp.second);
 }
 
 #ifndef CGAL_NO_OSTREAM_INSERT_POINTC2
diff --git a/Packages/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h b/Packages/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h
index 25a28d7164f..08f61a7ac43 100644
--- a/Packages/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h
+++ b/Packages/Cartesian_kernel/include/CGAL/Cartesian/Point_3.h
@@ -170,11 +170,10 @@ template < class R >
 Bbox_3
 PointC3<R>::bbox() const
 {
-  // FIXME: to_interval
-  double bx = CGAL::to_double(x());
-  double by = CGAL::to_double(y());
-  double bz = CGAL::to_double(z());
-  return Bbox_3(bx, by, bz, bx, by, bz);
+  std::pair<double,double> xp = CGAL::to_interval(x());
+  std::pair<double,double> yp = CGAL::to_interval(y());
+  std::pair<double,double> zp = CGAL::to_interval(z());
+  return Bbox_3(xp.first, yp.first, zp.first,  xp.second, yp.second, zp.second);
 }
 
 #ifndef CGAL_CARTESIAN_NO_OSTREAM_INSERT_POINTC3
diff --git a/Packages/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h b/Packages/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h
index 964cb6e2341..8b56ff32dea 100644
--- a/Packages/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h
+++ b/Packages/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h
@@ -23,6 +23,7 @@
 #define CGAL_CARTESIAN_SPHERE_3_H
 
 #include <CGAL/utility.h>
+#include <CGAL/Interval_arithmetic.h>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -279,14 +280,23 @@ template < class R >
 CGAL_KERNEL_INLINE
 Bbox_3
 SphereC3<R>::bbox() const
-{
-  double cx = CGAL::to_double(center().x());
-  double cy = CGAL::to_double(center().y());
-  double cz = CGAL::to_double(center().z());
-  double radius = CGAL::sqrt(CGAL::to_double(squared_radius()));
+{ 
+  Bbox_3 b = center().bbox();
 
-  return Bbox_3(cx - radius, cy - radius, cz - radius,
-                cx + radius, cy + radius, cz + radius);
+  Interval_nt<> x (b.xmin(), b.xmax());
+  Interval_nt<> y (b.ymin(), b.ymax());
+  Interval_nt<> z (b.zmin(), b.zmax());
+
+  Interval_nt<> sqr = CGAL::to_interval(squared_radius());
+  Interval_nt<> r = CGAL::sqrt(sqr);
+  Interval_nt<> minx = x-r;
+  Interval_nt<> maxx = x+r;
+  Interval_nt<> miny = y-r;
+  Interval_nt<> maxy = y+r;
+  Interval_nt<> minz = z-r;
+  Interval_nt<> maxz = z+r;
+
+  return Bbox_3(minx.inf(), miny.inf(), minz.inf(), maxx.sup(), maxy.sup(), maxz.sup());
 }
 
 /*