diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_plane_policies.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_plane_policies.h
index 842f16dd2d41..4eae0a738f3d 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_plane_policies.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_plane_policies.h
@@ -116,7 +116,10 @@ class Probabilistic_plane_quadric_calculator
                                 const Col_4& /*p0*/,
                                 const Col_4& /*p1*/) const
   {
-    // @fixme check this
+    // TODO: an all-zero matrix is just a specific case of a non-invertible matrix;
+    // shouldn't this rather assert that quadric is invertible?
+    CGAL_precondition(!quadric.isZero(0));
+
     return construct_optimal_point_invertible<GeomTraits>(quadric);
   }
 };
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_triangle_policies.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_triangle_policies.h
index 4be3f28c29c5..91104d5d8c5b 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_triangle_policies.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_triangle_policies.h
@@ -106,7 +106,9 @@ class Probabilistic_triangle_quadric_calculator
 
   Col_4 construct_optimal_point(const Mat_4& quadric, const Col_4& /*p0*/, const Col_4& /*p1*/) const
   {
-    // @fixme check this
+    // TODO: an all-zero matrix is just a specific case of a non-invertible matrix;
+    // shouldn't this rather assert that quadric is invertible?
+    CGAL_precondition(!quadric.isZero(0));
     return construct_optimal_point_invertible<GeomTraits>(quadric);
   }
 };
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_policy_base.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_policy_base.h
index d669e44f3178..41f6103cb8e2 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_policy_base.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/internal/GarlandHeckbert_policy_base.h
@@ -208,9 +208,6 @@ class GarlandHeckbert_cost_and_placement
     if(!placement)
       return boost::optional<typename Profile::FT>();
 
-    CGAL_precondition(!get(vcm(), profile.v0()).isZero(0));
-    CGAL_precondition(!get(vcm(), profile.v1()).isZero(0));
-
     const Mat_4 combined_matrix = combine_matrices(get(vcm(), profile.v0()),
                                                    get(vcm(), profile.v1()));
     const Col_4 pt = point_to_homogenous_column(*placement);
@@ -224,9 +221,6 @@ class GarlandHeckbert_cost_and_placement
   template <typename Profile>
   boost::optional<typename Profile::Point> operator()(const Profile& profile) const
   {
-    CGAL_precondition(!get(vcm(), profile.v0()).isZero(0));
-    CGAL_precondition(!get(vcm(), profile.v1()).isZero(0));
-
     // the combined matrix has already been computed in the evaluation of the cost...
     const Mat_4 combined_matrix = combine_matrices(get(vcm(), profile.v0()),
                                                    get(vcm(), profile.v1()));