Motivated by recent observations of coherent Ge island formation during growth of Ge on Si (100), we have carried out a theoretical study of the elastic energies associated with the evolution of a uniform strained overlayer as it segregates into coherent islands. In the context of a two-dimensional model, we have explored the conditions under which coherent islands may be energetically favored over both uniform epitaxial films and dislocated islands. We find that if the interface energy (for dislocated islands) is more than about 15% of the surface energy, then there is a range of island sizes for which the coherent island structure is preferred.