Submonolayer films of AE on Pt(111) exhibit parallel partial dislocations separated by narrow hcp domains and much wider fcc domains, the large difference in width being atypical of strained metal overlayers on close-packed substrates. Using a two-dimensional Frenkel-Kontorova model, we calculate the relative domain widths. We examine possible effects of dislocations on equilibrium island shape and calculate the energies of stable and metastable dislocation structures versus island size. Experimental results are explained by proximity to the incommensurate-commensurate phase transition. [S0031-9007(99)09291-1].