A semiempirical shell-correction method including ellipsoidal deformations is used to determine binding energies of open-shell, unpolarized He-3(N) clusters. Shell effects, shapes, and other ground-state properties (Like the chemical potential) are determined. He-3(N) clusters are found to be substantially Less deformed due to their relatively high surface energy as compared to that of alkali-metal clusters (e.g., sodium clusters), As a result, the size-evolutionary patterns associated with He-3(N) clusters are significantly different than the corresponding ones for Na-N clusters. In particular, odd-even oscillations and signatures of subshell closures are absent in the case of He-3(N) clusters, while they are prominent in the case of alkali-metal clusters.