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The average separation of two-dimensional islands in Cu(100) submonolayer homoepitaxy as a function of the deposition flux at 213 K has been studied using spot profile analysis low-energy electron diffraction. As the flux decreases, a large change in the apparent critical island size, from one to a value between seven and 12 atoms, is obtained even though the temperature is held constant. This is shown to be consistent with a recently proposed dimer shearing mechanism which has a significant influence on the stability of islands with eight atoms or less.