Recent experiments indicated that the formation of small, nonstoichiometric clusters ZnnSm and ZnnSm+ was possible. In this work, the ground states of these clusters, where 1 < n, m less than or equal to 4, were studied using density functional theory. Global minima were found to be primarily cyclic structures in which the S-Zn-S preference for large bond angles was preserved. Ionization was shown to lead to structural relaxation and occasionally major changes in conformation. Cohesive energies are reported as a function of cluster composition. Qualitative comparisons were extracted from the energetics resulting from structural optimizations, and such comparisons appear to be consistent with the experiment. The computational data for the ZnSn and ZnnSm (where m > n) clusters indicated that sulfur-sulfur bonding in larger ZnS clusters could be feasible without significant energetic cost and that such structures should at least be considered.