Strained island growth in lattice-mismatched epitaxial systems differs from relaxed island growth. The total elastic energy of a strained island changes its chemical potential and growth rate. This effect is investigated for an ensemble of misfitting coplanar hemispherical caps interacting through surface diffusion alone. A general expression for the growth rate of strained islands is obtained by including elastic energies in the driving force for Ostwald ripening. For the first time, to our knowledge, a coherent-to-incoherent transition is shown to dramatically affect ripening kinetics. Coherent islands are shown to grow more slowly than incoherent islands of the same radius. Consequently, the growth rate of an island accelerates when it dislocates at the coherent-to-incoherent transition in agreement with recent experimental observations.