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 b8aada2e36f..ce09e4f97af 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
@@ -120,10 +120,9 @@ std::size_t get_cell_corners(const Domain& domain,
     auto val = domain.value(v);
     // Avoiding singular cases.
 
-    if (val == isovalue) {
-      typename Domain::FT shift = (isovalue == 0) ? 0.00000001 : isovalue * 0.0000001;
-      val -= abs(shift);
-    }
+    if (abs(val - isovalue) < 0.00000001)
+      val = isovalue - 0.00000001;
+
     values[v_id] = val;
     if(values[v_id] >= isovalue)
       index.set(v_id);
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 5f94951c260..1ff9815fed6 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
@@ -868,7 +868,7 @@ private:
 
       calc_coordinates(values, idx, i0, a, b, c, d, f_flag, q_sol, ui, vi, wi);
 
-      if (!std::isfinite(ui[0]) || !std::isfinite(ui[1]))
+      if (!std::isfinite(CGAL::to_double(ui[0])) || !std::isfinite(CGAL::to_double(ui[1])))
         continue;
 
       break;
@@ -998,9 +998,10 @@ private:
       Point_index tg_idx[6];
       for(int i=0; i<6; ++i)
       {
-        const FT u = hvt[i][0];
-        const FT v = hvt[i][1];
-        const FT w = hvt[i][2];
+        const FT u = hvt[i][0] < 0.05 ? 0.05 : (hvt[i][0] > 0.95 ? 0.95 : hvt[i][0]);
+        const FT v = hvt[i][1] < 0.05 ? 0.05 : (hvt[i][1] > 0.95 ? 0.95 : hvt[i][1]);
+        const FT w = hvt[i][2] < 0.05 ? 0.05 : (hvt[i][2] > 0.95 ? 0.95 : hvt[i][2]);
+
         const FT px = (FT(1) - w) * ((FT(1) - v) * (x_coord(corners[0]) + u * (x_coord(corners[1]) - x_coord(corners[0]))) +
                                                v * (x_coord(corners[2]) + u * (x_coord(corners[3]) - x_coord(corners[2])))) +
                                 w * ((FT(1) - v) * (x_coord(corners[4]) + u * (x_coord(corners[5]) - x_coord(corners[4]))) +