Discrete dislocation plasticity simulations are performed to investigate the role of interaction between neighboring asperities on the contact pressure induced by a rigid platen on a rough surface. The rough surface is modeled as an array of equispaced asperities with a sinusoidal profile. The spacing between asperities is varied and the contact pressure necessary to flatten the surface to a given strain is computed. Plasticity in the asperities and in the crystal below is described by the collective glide of dislocations of edge character.