Results are presented of the magnetoresistance of MBE-grown (111) Co/Cu multilayers measured with the current perpendicular to the plane of the layers (CPP). Although for measurements made with the more common geometry of current in the plane of the layers (CIP) there are large differences between the results on samples made by sputtering and those prepared by MBE, for these new CPP data the results on samples made by the two techniques are very much alike. For copper layers with thicknesses between 0.9nm to 6nm the magnetoresistance shows oscillations with copper thickness that were almost non-existent in the earlier CIP data. At the second peak the magnetoresistance in the CPP geometry is an order of magnitude greater than that in the CIP configuration. Although the interfaces in these samples have been shown to be very sharp, they appear to form a mosaic structure with the antiferromagnetic regions embedded in a ferromagnetic structure. It is argued that for CIP measurements the GMR is greatly reduced by these ferromagnetic correlations over lengthscales long compared to the electron mean free path. For CPP measurements, on the other hand, it is the spin diffusion length that is the determining factor with the mean free path no longer a key parameter and with values of the GMR virtually independent of the growth process.