diff --git a/Mesh_3/doc/Mesh_3/Concepts/MeshDomain_3.h b/Mesh_3/doc/Mesh_3/Concepts/MeshDomain_3.h
index e91c09e2a4b..e96dfa58b46 100644
--- a/Mesh_3/doc/Mesh_3/Concepts/MeshDomain_3.h
+++ b/Mesh_3/doc/Mesh_3/Concepts/MeshDomain_3.h
@@ -178,6 +178,15 @@ typedef unspecified_type Construct_intersection;
 
 /// @}
 
+/// \name Bounding box
+/// Since CGAL-4.8, a model of `MeshDomain_3` must provide a function
+/// providing a bounding box of the domain.
+/// @{
+
+/// Return the bounding box of the domain
+Bbox_3 bbox() const;
+/// @}
+
 /// \name Operations
 /// The following functions give access to the function objects:
 /// @{
diff --git a/Mesh_3/include/CGAL/Implicit_mesh_domain_3.h b/Mesh_3/include/CGAL/Implicit_mesh_domain_3.h
index 5adbe5b7e30..1801e8b3729 100644
--- a/Mesh_3/include/CGAL/Implicit_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Implicit_mesh_domain_3.h
@@ -74,7 +74,7 @@ public:
   /// Destructor
   virtual ~Implicit_mesh_domain_3() {}
 
-
+  using Base::bbox;
 private:
   // Disabled copy constructor & assignment operator
   typedef Implicit_mesh_domain_3<Function,BGT> Self;
diff --git a/Mesh_3/include/CGAL/Labeled_image_mesh_domain_3.h b/Mesh_3/include/CGAL/Labeled_image_mesh_domain_3.h
index 62eefd5afe6..4b24a848550 100644
--- a/Mesh_3/include/CGAL/Labeled_image_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Labeled_image_mesh_domain_3.h
@@ -77,6 +77,7 @@ public:
   /// Destructor
   virtual ~Labeled_image_mesh_domain_3() {}
 
+  using Base::bbox;
 
 private:
   /// Returns a box enclosing image \c im
diff --git a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
index f7924b68188..7d85d1bad97 100644
--- a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
@@ -142,6 +142,13 @@ public:
     return Construct_initial_points(*this);
   }
 
+  /**
+   * Returns a bounding box of the domain
+   */
+  Bbox_3 bbox() const {
+    return bbox_.bbox();
+  }
+
   /**
    * Returns true if point~\ccc{p} is in the domain. If \ccc{p} is in the
    *  domain, the parameter index is set to the index of the subdomain
diff --git a/Mesh_3/include/CGAL/Mesh_3/Labeled_mesh_domain_3.h b/Mesh_3/include/CGAL/Mesh_3/Labeled_mesh_domain_3.h
index 39713d977c6..52e4c47cbc7 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Labeled_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Labeled_mesh_domain_3.h
@@ -118,6 +118,13 @@ public:
       delete p_rng_;
   }
 
+  /**
+   * Returns a bounding box of the domain
+   */
+  Bbox_3 bbox() const {
+    return this->bbox_.bbox();
+  }
+
   /**
    * Constructs  a set of \ccc{n} points on the surface, and output them to
    *  the output iterator \ccc{pts} whose value type is required to be
diff --git a/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h b/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h
index b9ef1c603c8..04a236ab8a4 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Mesher_3.h
@@ -484,27 +484,11 @@ initialize()
 #if defined(CGAL_LINKED_WITH_TBB) || \
     defined(CGAL_SEQUENTIAL_MESH_3_ADD_OUTSIDE_POINTS_ON_A_FAR_SPHERE)
 
-  Bbox_3 estimated_bbox;
-  CGAL_assertion_code(bool is_estimated_bbox_initialized = false);
-
 #ifndef CGAL_SEQUENTIAL_MESH_3_ADD_OUTSIDE_POINTS_ON_A_FAR_SPHERE
   if(boost::is_convertible<Concurrency_tag, Parallel_tag>::value)
 #endif // If that macro is defined, then estimated_bbox must be initialized
   {
-    typedef std::vector<std::pair<Point, Index> > Points_vector;
-    Points_vector random_points_on_surface;
-    r_oracle_.construct_initial_points_object()(
-                                                std::back_inserter(random_points_on_surface), 1000);
-    typename Points_vector::const_iterator
-      it = random_points_on_surface.begin(),
-      it_end = random_points_on_surface.end();
-    estimated_bbox = it->first.bbox();
-    ++it;
-    for( ; it != it_end ; ++it)
-      estimated_bbox = estimated_bbox + it->first.bbox();
-
-    Base::set_bbox(estimated_bbox);
-    CGAL_assertion_code(is_estimated_bbox_initialized = true);
+    Base::set_bbox(r_oracle_.bbox());
   }
 #endif // CGAL_LINKED_WITH_TBB||"sequential use far sphere"
 
@@ -523,8 +507,7 @@ initialize()
 
     if (r_c3t3_.number_of_far_points() == 0 && r_c3t3_.number_of_facets() == 0)
     {
-      CGAL_assertion(is_estimated_bbox_initialized);
-      const Bbox_3 &bbox = estimated_bbox;
+      const Bbox_3 &bbox = r_oracle_.bbox();
 
       // Compute radius for far sphere
       const double xdelta = bbox.xmax()-bbox.xmin();
diff --git a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
index 5e37b177149..13ffb75e30d 100644
--- a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
@@ -367,6 +367,14 @@ public:
   }
 
 
+  /**
+   * Returns a bounding box of the domain
+   */
+  Bbox_3 bbox() const {
+    return tree_.bbox();
+  }
+
+
   /**
    * Returns true if point~\ccc{p} is in the domain. If \ccc{p} is in the
    *  domain, the parameter index is set to the index of the subdomain