The energetics of island growth on thin semiconducting films deposited on lattice-mismatched substrates is discussed in this article. Hut clusters similar to those proposed by Mo et al. [Phys. Rev. Lett. 65, 1020 (1990)] for Ge/Si(001), with (10n), (n greater than or equal to 3), or (11n), (n greater than or equal to 1), side facets will be analyzed. Results show that hut clusters are the energetically favorable structures during early growth, with side facets of rebonded (105) planes; at later times, larger islands with (11n)-like facets become favorable. It is found that islands nucleate with critical nuclei of about 1 atom and grow two dimensionally until they reach a critical size s(c), when it is favorable for the islands to become three dimensional. There is an effective barrier at the transition from two dimensional to three dimensional growth. Beyond the barrier, there is an immediate energy gain which can be large, on the order of 5-10 meV/atom for the highly mismatched system of InAs/GaAs. It is suggested that these results are the underlying reason for the uniformity seen in self-assembled quantum dots in highly mismatched heteroepitaxy.