The occurrence of an Ag layer on top of a Cu (111) substrate can result from either deposition (Ag/Cu) or strong segregation at the surface of a dilute Cu(Ag) alloy. Molecular dynamics simulations within many-body tight-binding potentials show that two structures compete: one corresponding to a rather uniform Ag (111) layer on top of a Cu (111) substrate leading to a Moire structure and the other involving constitutive vacancies forming triangular loops of partial dislocations in the first Cu substrate layer. A useful guide to predict the most efficient relaxation mechanism is to characterize the regions which undergo the largest stress. Thus, the local pressure map in the first Cu underlayer allows to predict a complementarity between the segregation of vacancies in compressive sites and the Ag enrichment, due to the larger atomic radius of the Ag atoms, in the tensile ones. Segregation energy maps, both for vacancies and Ag atoms, confirm this prediction and lead to several perspectives for the kinetics of dissolution of an Ag deposit over a Cu (111) substrate.