We have performed a grazing incidence x-ray diffraction study of the self-organized N/Cu(001) system. Diffraction satellites associated with self-organization are particularly intense around Bragg conditions of the bulk crystal. Bulk elastic relaxations due to surface stress discontinuities at domain boundaries are responsible for this feature. A quantitative analysis shows that these relaxations, computed by molecular dynamics or continuum elasticity, explain very well the whole diffraction study. A difference in surface stress of 7 N m(-1) between uncovered and N-covered regions of the Cu surface is shown to be the driving force for self-organization.