The application of spectral methods to the software clustering problem has the advantage of producing results that are within a known factor of the optimal solution. Heuristic search methods, such as those supported by the Bunch clustering tool, only guarantee local optimality which may be far from the global optimum. In this paper, we apply the spectral methods to the software clustering problem and make comparisons to Bunch using the same clustering criterion. We conducted a case study, involving 13 software systems, to draw our comparisons. There is a dual benefit to making these comparisons. Specifically, we gain insight into (1) the quality of the spectral methods solutions; and (2) the proximity of the results produced by Bunch to the optimal solution.