  A method is presented to obtain {\it ab initio} upper and lower bounds to
surface energies of stress-driven discommensurate surface structures, possibly
non-periodic or exhibiting very large unit cells. The instability of the
stressed, commensurate parent of the discommensurate structure sets an upper
bound to its surface energy; a lower bound is defined by the surface energy of
an ideally commensurate but laterally strained hypothetical surface system. The
surface energies of the phases of the Si(111):Ga and Ge(111):Ga systems and the
energies of the discommensurations are determined within $\pm 0.2$ eV.
