diff --git a/Isosurfacing_3/examples/Isosurfacing_3/marching_cubes_strategies.cpp b/Isosurfacing_3/examples/Isosurfacing_3/marching_cubes_strategies.cpp
index 15487eecb80..38ad1261158 100644
--- a/Isosurfacing_3/examples/Isosurfacing_3/marching_cubes_strategies.cpp
+++ b/Isosurfacing_3/examples/Isosurfacing_3/marching_cubes_strategies.cpp
@@ -84,7 +84,7 @@ int main(int argc, char** argv)
     std::cout << "Output #vertices: " << points.size() << std::endl;
     std::cout << "Output #triangles: " << triangles.size() << std::endl;
     std::cout << "Elapsed time: " << timer.time() << " seconds" << std::endl;
-    CGAL::IO::write_polygon_soup("marching_cubes.off", points, triangles);
+    CGAL::IO::write_polygon_soup("marching_cubes_TMC.off", points, triangles);
   }
 
   std::cout << "Done" << std::endl;
diff --git a/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/marching_cubes_functors.h b/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/marching_cubes_functors.h
index c079609d138..9ac3d395d5a 100644
--- a/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/marching_cubes_functors.h
+++ b/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/marching_cubes_functors.h
@@ -278,13 +278,18 @@ public:
     CGAL_precondition(m_domain.cell_vertices(cell).size() == 8);
     CGAL_precondition(m_domain.cell_edges(cell).size() == 12);
 
-    std::array<FT, 8> values;
-    std::array<Point_3, 8> corners;
-    const int i_case = get_cell_corners(m_domain, cell, m_isovalue, corners, values);
+    // @todo for SDFs, we could query at the center of the voxel an early exit
+
+    constexpr std::size_t vpc = Domain::VERTICES_PER_CELL;
+
+    std::array<FT, vpc> values;
+    std::array<Point_3, vpc> corners;
+    const std::size_t i_case = get_cell_corners(m_domain, cell, m_isovalue, corners, values);
 
     // skip empty cells
-    const int all_bits_set = (1 << (8 + 1)) - 1; // last 8 bits are 1
-    if(i_case == 0 || i_case == all_bits_set)
+    constexpr std::size_t ones = (1 << vpc) - 1;
+    if((i_case & ones) == ones || // all bits set
+       (i_case & ones) == 0) // no bits set
       return;
 
     std::array<Point_3, 12> vertices;
diff --git a/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/topologically_correct_marching_cubes_functors.h b/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/topologically_correct_marching_cubes_functors.h
index 61cf2d78a79..9a72fb43d51 100644
--- a/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/topologically_correct_marching_cubes_functors.h
+++ b/Isosurfacing_3/include/CGAL/Isosurfacing_3/internal/topologically_correct_marching_cubes_functors.h
@@ -128,7 +128,7 @@ public:
   {
     std::array<FT, 8> values;
     std::array<Point_3, 8> corners;
-    const int i_case = get_cell_corners(m_domain, cell, m_isovalue, corners, values);
+    const std::size_t i_case = get_cell_corners(m_domain, cell, m_isovalue, corners, values);
 
     // this is the only difference to mc
     const int tcm = Cube_table::t_ambig[i_case];
@@ -142,8 +142,9 @@ public:
 #endif
     }
 
-    constexpr int all_bits_set = (1 << (8 + 1)) - 1;  // last 8 bits are 1
-    if(i_case == 0 || i_case == all_bits_set)
+    constexpr std::size_t ones = (1 << 8) - 1;
+    if((i_case & ones) == ones || // all bits set
+       (i_case & ones) == 0) // no bits set
       return;
 
     std::array<Point_3, 12> vertices;