Bakhvalov (B) and Shishkin (S) meshes are used very often to discretize singular perturbation problems. The smoother B meshes are more complicated than the piecewise equidistant S meshes, but their considerably better accuracy usually outweighs this. In this paper, we point out that the real advantage of S meshes comes to light when constructing higher-order discretizations. We show this by considering an almost third-order finite-difference scheme for a semilinear problem with two small parameters.