This brief article presents a simple modification to the widely-used Kausel-Roësset Stiffness Matrix Method (SMM), and in particular to its implementation in the context of the Thin-Layer Method (TLM). This modification allows making fast and accurate computations of wavenumber spectra even for layered media underlain by infinitely deep half-spaces. As is well known, the TLM uses a finite element expansion in the depth direction, which in principle disallows exact representations of infinitely deep media other than through Paraxial Approximations or Perfectly Matched Layers. However, with the modification presented herein, that obstacle is removed. The very simple method is first presented and then demonstrated by means of examples involving layered half-spaces. © 2016 Elsevier Ltd