AbstractTins paper considers recently developed theoretical, closed form re-sults which permit the detailed analysis of a popular robust signal detector for nominally Laplace i.i.d. noise. Although the theoretical results hold for arbitrary sample sizes, the evaluation of these results can require lengthy computation times for even intermediate sample sizes. For this reason, a simulation analysis of this robust detector may be more practical. This paper demonstrates that importance sampling can significantly speed (as compared to conventional Monte Carlo techniques) the simulation time required for estimating the smaller false alarm probabilities. Furthermore, the theoretical results can be used to compare the effectiveness of the importance sampling simulation technique. However, one drawback to importance sampling is that it requires an exact knowledge of the input statistics.