We demonstrate that the concept of mesoscopic misfit, rather than macroscopic misfit, should be used to describe the atomistic processes in the early stages of metal heteroepitaxy. Atomic scale calculations reveal the drastic effect of the mesoscopic misfit on strain in Co islands on the Cu(001) surface. We show that atomic motion on strained islands is strongly affected by the mesoscopic misfit and depends on the size of the islands. The diffusion coefficient on top of small islands is found to be larger by 2 orders of magnitude than that on large islands.