diff --git a/Kinetic_space_partition/include/CGAL/KSP/debug.h b/Kinetic_space_partition/include/CGAL/KSP/debug.h
index 71ce02aed30..6c8cce2838a 100644
--- a/Kinetic_space_partition/include/CGAL/KSP/debug.h
+++ b/Kinetic_space_partition/include/CGAL/KSP/debug.h
@@ -320,7 +320,7 @@ public:
   using Segment_2 = typename Traits::Segment_2;
   using Segment_3 = typename Traits::Segment_3;
 
-  using Color        = CGAL::Color;
+  using Color        = CGAL::IO::Color;
   using Surface_mesh = CGAL::Surface_mesh<Point_3>;
   using Random       = CGAL::Random;
 
diff --git a/Kinetic_space_partition/include/CGAL/KSP/utils.h b/Kinetic_space_partition/include/CGAL/KSP/utils.h
index 84a380bdb60..7a39034a8a8 100644
--- a/Kinetic_space_partition/include/CGAL/KSP/utils.h
+++ b/Kinetic_space_partition/include/CGAL/KSP/utils.h
@@ -117,7 +117,7 @@ template<typename ResultType, typename Type1, typename Type2>
 inline const ResultType intersection(const Type1& t1, const Type2& t2) {
 
   ResultType out;
-  const bool is_intersection_found = intersection(t1, t2, out);
+  CGAL_assertion_code(const bool is_intersection_found =) intersection(t1, t2, out);
   CGAL_assertion(is_intersection_found);
   return out;
 }
diff --git a/Kinetic_space_partition/include/CGAL/KSP_2/Data_structure.h b/Kinetic_space_partition/include/CGAL/KSP_2/Data_structure.h
index 232c5796e0d..f6a2c9f78d6 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_2/Data_structure.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_2/Data_structure.h
@@ -39,10 +39,10 @@ public:
   typedef typename Kernel::Segment_2 Segment_2;
 
   typedef Support_line<Kernel> Support_line_DS;
-  typedef Segment Segment;
-  typedef Vertex<FT> Vertex;
 
-  typedef Meta_vertex<Point_2> Meta_vertex;
+  typedef CGAL::KSP_2::internal::Vertex<FT> Vertex;
+  typedef CGAL::KSP_2::internal::Segment Segment;
+  typedef CGAL::KSP_2::internal::Meta_vertex<Point_2> Meta_vertex;
 
   typedef std::vector<Support_line_DS> Support_lines;
   typedef std::vector<Segment> Segments;
@@ -573,9 +573,6 @@ public:
           < position_of_meta_vertex_on_support_line(b, support_line_idx));
       });
 
-    std::size_t nb_segments_before = m_segments.size();
-    std::size_t nb_vertices_before = m_vertices.size();
-
     // Attach to existing endpoint
     std::size_t new_target_idx = m_vertices.size();
     m_vertices.push_back(Vertex(position_of_meta_vertex_on_support_line(meta_vertices_idx.front(),
diff --git a/Kinetic_space_partition/include/CGAL/KSP_2/Event_queue.h b/Kinetic_space_partition/include/CGAL/KSP_2/Event_queue.h
index c7db26b73b9..b75d4be4dc3 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_2/Event_queue.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_2/Event_queue.h
@@ -34,7 +34,7 @@ public:
   typedef GeomTraits Kernel;
   typedef typename Kernel::FT FT;
 
-  typedef Event<GeomTraits> Event;
+  typedef CGAL::KSP_2::internal::Event<GeomTraits> Event;
 
 private:
 
diff --git a/Kinetic_space_partition/include/CGAL/KSP_3/Data_structure.h b/Kinetic_space_partition/include/CGAL/KSP_3/Data_structure.h
index 1321f651131..20fca11ef22 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_3/Data_structure.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_3/Data_structure.h
@@ -816,7 +816,7 @@ public:
       const bool is_inserted = pair.second;
       if (is_inserted) {
         typename Intersection_kernel::Line_3 line;
-        bool intersect = intersection(plane, m_support_planes[common_bbox_plane_idx].exact_plane(), line);
+        CGAL_assertion_code(bool intersect =)  intersection(plane, m_support_planes[common_bbox_plane_idx].exact_plane(), line);
         CGAL_assertion(intersect);
         pair.first->second = m_intersection_graph.add_line(line);
       }
@@ -1251,7 +1251,7 @@ public:
 
     typename Intersection_kernel::Line_3 line;
     auto it = support_planes_idx.begin();
-    bool intersect = intersection(m_support_planes[*it++].exact_plane(), m_support_planes[*it++].exact_plane(), line);
+    CGAL_assertion_code(bool intersect =) intersection(m_support_planes[*it++].exact_plane(), m_support_planes[*it++].exact_plane(), line);
     CGAL_assertion(intersect);
 
     std::size_t line_idx = m_intersection_graph.add_line(line);
diff --git a/Kinetic_space_partition/include/CGAL/KSP_3/Initializer.h b/Kinetic_space_partition/include/CGAL/KSP_3/Initializer.h
index 097aca60b31..15a3acc355c 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_3/Initializer.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_3/Initializer.h
@@ -192,8 +192,8 @@ private:
     // Loop complete, connecting face with all edges.
     for (IEdge edge : face.edges) {
       m_data.support_plane(sp_idx).add_neighbor(edge, face_idx);
-      IFace f1 = m_data.support_plane(sp_idx).iface(edge);
-      IFace f2 = m_data.support_plane(sp_idx).other(edge, f1);
+      CGAL_assertion_code(IFace f1 = m_data.support_plane(sp_idx).iface(edge);)
+      CGAL_assertion_code(IFace f2 = m_data.support_plane(sp_idx).other(edge, f1);)
       CGAL_assertion(f1 == face_idx || f2 == face_idx);
     }
 
@@ -590,14 +590,14 @@ private:
             }
           }
           if (!outside) {
-            if (face == -1)
+            if (face == IFace(-1))
               face = f;
             else {
               std::cout << "Two faces found for " << sp_idx << " sp, f1 " << face << " f2 " << f << std::endl;
             }
           }
         }
-        if (face != -1) {
+        if (face != IFace(-1)) {
           if (!m_data.igraph().face(face).part_of_partition) {
             auto pface = m_data.add_iface_to_mesh(sp_idx, face);
             sp.data().initial_ifaces.push_back(face);
diff --git a/Kinetic_space_partition/include/CGAL/KSP_3/Support_plane.h b/Kinetic_space_partition/include/CGAL/KSP_3/Support_plane.h
index cf842090bb8..2a694c597dc 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_3/Support_plane.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_3/Support_plane.h
@@ -150,8 +150,7 @@ public:
         static_cast<FT>(point.y()),
         static_cast<FT>(point.z())));
     }
-    const std::size_t n = points.size();
-    CGAL_assertion(n == polygon.size());
+    CGAL_assertion(points.size() == polygon.size());
 
     From_exact from_exact;
 
@@ -232,7 +231,7 @@ public:
         from_exact(point.y()),
         from_exact(point.z())));
     }
-    const std::size_t n = points.size();
+    CGAL_assertion_code(const std::size_t n = points.size();)
     CGAL_assertion(n == polygon.size());
     CGAL_assertion(n != 0);