Deposition of Pb on Cu(111) prior to the growth of Co/Cu superlattices changes the magnetic properties of the latter. The use of a surfactant induces layer-by-layer growth of Co and delays the fcc to hcp structural transition. As a consequence, the easy axis of magnetization remains perpendicular to the plane for Co/Cu films grown with Pb. On the other hand, the elimination of twinning in the Cu spacers grown with surfactants allows the observation of complete antiferromagnetic coupling in Co/Cu superlattices for both in-plane and out-of-plane magnetization.