diff --git a/Kinetic_data_structures/examples/Kinetic_data_structures/Delaunay_triangulation_3.C b/Kinetic_data_structures/examples/Kinetic_data_structures/Delaunay_triangulation_3.C
index e025fd651a3..cd670d4291e 100644
--- a/Kinetic_data_structures/examples/Kinetic_data_structures/Delaunay_triangulation_3.C
+++ b/Kinetic_data_structures/examples/Kinetic_data_structures/Delaunay_triangulation_3.C
@@ -14,7 +14,7 @@ int main(int , char *[])
 
     Traits::Simulator::Handle sp= tr.simulator_handle();
 
-    std::ifstream in("data/points_3");
+    std::ifstream in("data/points_3.small");
     in >> *tr.active_points_3_table_handle();
 
     kdel.set_has_certificates(true);
diff --git a/Kinetic_data_structures/include/CGAL/Kinetic/Cartesian_kinetic_kernel.h b/Kinetic_data_structures/include/CGAL/Kinetic/Cartesian_kinetic_kernel.h
index 05bf085df14..5512a39da6b 100644
--- a/Kinetic_data_structures/include/CGAL/Kinetic/Cartesian_kinetic_kernel.h
+++ b/Kinetic_data_structures/include/CGAL/Kinetic/Cartesian_kinetic_kernel.h
@@ -38,6 +38,7 @@ Cartesian_kinetic_kernel<Function_kernel_k> >
     typedef internal::Cartesian_kinetic_kernel_base<Function_kernel_k,
         Cartesian_kinetic_kernel<Function_kernel_k> > P;
     public:
+  typedef Function_kernel_k Function_kernel;
         Cartesian_kinetic_kernel(Function_kernel_k pk): P(pk){}
         Cartesian_kinetic_kernel(){}
 };
diff --git a/Kinetic_data_structures/include/CGAL/Kinetic/Delaunay_triangulation_2.h b/Kinetic_data_structures/include/CGAL/Kinetic/Delaunay_triangulation_2.h
index a5c04dfdc58..e3e4e613b3d 100644
--- a/Kinetic_data_structures/include/CGAL/Kinetic/Delaunay_triangulation_2.h
+++ b/Kinetic_data_structures/include/CGAL/Kinetic/Delaunay_triangulation_2.h
@@ -460,10 +460,10 @@ protected:
   }
 
   bool is_hull_edge(const Edge &e) const {
-    return !TDS_helper::mirror_vertex(e)->point() 
-      || !TDS_helper::third_vertex(e)->point()
-      || !TDS_helper::origin(e)->point()
-      || !TDS_helper::destination(e)->point();
+    return !static_cast<bool>(TDS_helper::mirror_vertex(e)->point())
+      || !static_cast<bool>(TDS_helper::third_vertex(e)->point())
+      || !static_cast<bool>(TDS_helper::origin(e)->point())
+      || !static_cast<bool>(TDS_helper::destination(e)->point());
   }
 
   SOC_certificate compute_failure_time(const Edge &e) const {
@@ -517,7 +517,7 @@ protected:
     CGAL_precondition(!TDS_helper::get_undirected_edge_label(e));
     Event_key k;
 
-    if (is_hull_edge(e)) {
+    if (static_cast<bool>(is_hull_edge(e))) {
       O2_certificate s= compute_hull_failure_time(e);
       Time t= s.failure_time();
       s.pop_failure_time();
diff --git a/Kinetic_data_structures/include/CGAL/Kinetic/Delaunay_triangulation_3.h b/Kinetic_data_structures/include/CGAL/Kinetic/Delaunay_triangulation_3.h
index 5d612ff3f54..3d6ca40bf2f 100644
--- a/Kinetic_data_structures/include/CGAL/Kinetic/Delaunay_triangulation_3.h
+++ b/Kinetic_data_structures/include/CGAL/Kinetic/Delaunay_triangulation_3.h
@@ -81,7 +81,7 @@ private:
     typedef typename TraitsT::Kinetic_kernel::Positive_orientation_3 Positive_orientation_3;
     typedef internal::Delaunay_3_edge_flip_event<This,
 						 typename Positive_side_of_oriented_sphere_3::result_type,
-						 typename TriangulationT::Edge> Edge_flip;;
+						 typename TriangulationT::Edge> Edge_flip;
     typedef typename internal::Delaunay_3_facet_flip_event<This, typename Positive_side_of_oriented_sphere_3::result_type,
 							   typename TriangulationT::Facet> Facet_flip;
 
diff --git a/Kinetic_data_structures/include/CGAL/Kinetic/Regular_triangulation_3.h b/Kinetic_data_structures/include/CGAL/Kinetic/Regular_triangulation_3.h
index 5d1b459ad40..365464c731d 100644
--- a/Kinetic_data_structures/include/CGAL/Kinetic/Regular_triangulation_3.h
+++ b/Kinetic_data_structures/include/CGAL/Kinetic/Regular_triangulation_3.h
@@ -717,7 +717,7 @@ public:
 	    CGAL_KINETIC_LOG(LOG_LOTS, "On init " << *kit << " is redundant" << std::endl);
 	    typename Triangulation::Cell_handle h= kdel_.triangulation().locate(*kit);
 	    redundant_points_[*kit]= make_certificate(*kit, h);
-	    redundant_cells_.insert(make_pair(h, *kit));
+	    redundant_cells_.insert(typename RCMap::value_type(h, *kit));
 	  }
 	}
       }
diff --git a/Kinetic_data_structures/include/CGAL/Kinetic/internal/Delaunay_triangulation_base_3.h b/Kinetic_data_structures/include/CGAL/Kinetic/internal/Delaunay_triangulation_base_3.h
index 0ecf664d375..3519e192ed0 100644
--- a/Kinetic_data_structures/include/CGAL/Kinetic/internal/Delaunay_triangulation_base_3.h
+++ b/Kinetic_data_structures/include/CGAL/Kinetic/internal/Delaunay_triangulation_base_3.h
@@ -1217,14 +1217,14 @@ public:
     int hinf=-1;
     for (unsigned int i=0; i<4; ++i) {
       Point_key k= f.first->vertex(i)->point();
-      if (!k) {
+      if (!static_cast<bool>(k)) {
 	hinf=i;
 	break;
       }
     }
     if (hinf==-1) {
       Point_key k= triangulation_.mirror_vertex(f.first, f.second)->point();
-      if ( !k ) {
+      if ( !static_cast<bool>(k) ) {
 	hinf=4;
       }
     }
diff --git a/Kinetic_data_structures/include/CGAL/Polynomial/Polynomial.h b/Kinetic_data_structures/include/CGAL/Polynomial/Polynomial.h
index 26977cc1eaa..83aa461897f 100644
--- a/Kinetic_data_structures/include/CGAL/Polynomial/Polynomial.h
+++ b/Kinetic_data_structures/include/CGAL/Polynomial/Polynomial.h
@@ -43,7 +43,7 @@ class Polynomial: public internal::Polynomial_impl<Polynomial<NTT>, NTT>
 
 // friend class internal::Polynomial_impl<This, NTT>; // NOT SO CLEAN
 
-#ifndef NDEBUG
+#ifdef CGAL_POLYNOMIAL_STRING
     typedef std::string Approximation;
     void generate_approximation() const
     {
@@ -56,7 +56,7 @@ class Polynomial: public internal::Polynomial_impl<Polynomial<NTT>, NTT>
 
     void approximate() const
     {
-#ifndef NDEBUG
+#ifdef CGAL_POLYNOMIAL_STRING
         generate_approximation();
 #endif
     }
@@ -72,14 +72,14 @@ class Polynomial: public internal::Polynomial_impl<Polynomial<NTT>, NTT>
 
 //! Default
         Polynomial() {
-#ifndef NDEBUG
+#ifdef CGAL_POLYNOMIAL_STRING
             approximation_="Not initialized.";
 #endif
         }
 
 //! Make a constant polynomial
         Polynomial(const NTT& c): Parent(c) {
-#ifndef NDEBUG
+#ifdef CGAL_POLYNOMIAL_STRING
             approximate();
 #endif
             strip_leading_zeros();
@@ -89,14 +89,14 @@ class Polynomial: public internal::Polynomial_impl<Polynomial<NTT>, NTT>
         template<typename Iterator>
             Polynomial(Iterator first, Iterator beyond)
         : Parent(first,beyond) {
-#ifndef NDEBUG
+#ifdef CGAL_POLYNOMIAL_STRING
             approximate();
 #endif
             strip_leading_zeros();
         }
 
         Polynomial(const Parent &p): Parent(p) {
-#ifndef NDEBUG
+#ifdef CGAL_POLYNOMIAL_STRING
             approximate();
 #endif
             strip_leading_zeros();
@@ -125,7 +125,7 @@ class Polynomial: public internal::Polynomial_impl<Polynomial<NTT>, NTT>
         }
 
     private:
-#ifndef NDEBUG
+#ifdef CGAL_POLYNOMIAL_STRING
 /*! A string represneting the approximation of the polynomial. For
   inspection in the debugger.*/
         mutable Approximation approximation_;