We present theoretical studies of two methods to produce stable island arrays. In height-constrained Stranski-Krastanov growth, we show that placing a ceiling above a thin film during annealing can reverse the role of elasticity, which normally causes the islands to coarsen. With elastic and surface energies providing refining and coarsening actions, respectively, it is possible to obtain equilibrium island sizes. In lithographically-induced self-assembly, the two competing forces are electrostatic and surface energies. Motivated by experimental observations of stable island arrays, we present an explanation for the stability. The electrostatic energy serves as the refining force while surface energy remains the usual coarsening agent. The two theories suggests a few experimentally controllable parameters that can be tuned to obtain the desired stable island diameters.