A study has been carried out of the effect of interface scattering on the magnitude of the giant magnetoresistance (MR) of MBE-grown Co/Cu superlattices. The authors find that increasing interface scattering by annealing the Co/Cu superlattice leads to a progressive decrease in the magnitude of the MR. In contrast to their results, it was recently reported that annealing increases the MR for Fe/Cr superlattices. An explanation is presented in terms of the spin dependence of interface scattering which accounts both for their data for the Co/Cu system, as well as for the opposite results obtained for the Fe/Cr system.