While toluene and iodotoluene binding to T4 lysozyme might not seem to be particularly relevant to drug discovery problems, the problem confronted here actually has considerable similarity to problems encountered in fragment based drug discovery (FBDD). FBDD attempts to find promising leads for early stage drug discovery by studying the binding of very small, often relatively rigid, ligands. These ligands can in fact be of relatively similar size and rigidity to toluene in some cases. Thus, prediction of binding modes of small rigid fragments is in fact of considerable interest. Additionally, even when structural data is available for the binding of fragments, the X-ray crystal structures obtained from FBDD campaigns sometimes have ambiguous electron density for the ligand, making the binding mode difficult to determine. Applying this NCMC method to cases involving rigid ligands could help determine the major binding mode(s) and/or resolve ambiguity in experimental structural data.