The diffusion constant of an adsorbed atom changes if the surface is under strain. Because of this, it is reasonable to expect that all diffusion-dependent phenomena occur differently on a strained surface. Here we study how homogeneous, metal-on-metal epitaxy is modified when it takes place on a (100) surface on which we have imposed a periodic inhomogeneous strain field. The periodic field studied here has square symmetry and a period of a hundred lattice sites. The strain is such that an atom diffusing on the surface has a tendency to drift toward the center of the unit cell of the strain field. We deposit atoms on this surface, up to a coverage of 0.15 atoms/site; then we stop deposition and allow the ensemble of islands formed during deposition to coarsen. If the deposition flux and the temperature of the surface are chosen properly, the ensemble of islands generated by this procedure is nearly periodic in space and has a greatly improved island-size uniformity.