We have used UHV dc magnetron sputtering to deposit giant magnetoresistive Co-Cu multilayers on Si substrates. The largest magnetoresistances are obtained in films which are deposited using the lowest sputtering pressures, and which therefore experience the most energetic bombardment during deposition. The large magnetoresistances are caused not by comparatively small resistivities in an applied magnetic field, but by relatively large zero-field resistivities. Structural features associated with low sputtering pressures allow substantial antiferromagnetic alignment of Co layers in zero field. The smaller the sputtering pressure, the greater the antiferromagnetic alignment, the greater the zero-field resistivity and the further the sample resistivity is able to fall when a magnetic field changes the alignment from antiferromagnetic to ferromagnetic. Multilayers of Co-Cu made by evaporation may not show substantial magnetoresistance because, unlike sputtering, evaporation transfers little energy to the instantaneous surface of a growing film.