Zinc sulfide clusters produced by direct laser ablation and analyzed in a time-of-flight mass-spectrometer, showed evidence that clusters composed of 3, 6, and 13 monomer units were ultrastable. The geometry and energies of neutral and positively charged ZnnSn clusters, up to n = 16, were obtained computationally at the B3LYP/6-311+G* level of theory with the assistance of an algorithm to generate all possible structures having predefined constraints. Small neutral and positive clusters were found to have planar geometries, neutral three-dimensional clusters have the geometry of closed-cage polyhedra, and cationic three-dimensional clusters have structures with a pair of two-coordinated atoms. Physical properties of the clusters as a function of size are reported. The relative stability of the positive stoichiometric clusters provides a thermodynamic rationale for the experimental results.