Upon annealing above 620 K, submonolayers of Ag deposited on Pt(111) are known to mix into the first surface layer. Thereby the individual Ag atoms reduce the strain fields caused by the lattice mismatch. As observed by scanning tunneling microscopy, careful annealing of the intermixed surface leads to the formation of small round islands with a preferential diameter of 150-300 Angstrom on terraces wider than a critical width of about 400 Angstrom. This indicates that the microscopically intermixed surface is still under considerable stress, which is released by a mesoscopic change of the morphology. An effective release of elastic stress at the island and step edges is thought to compensate for the formation energy of steps and the repulsive elastic step-step interaction.