Co/Cu/Co sandwiches were grown by molecular beam epitaxy onto a Cu(100) crystal with the intervening Cu layer fabricated to be wedge shaped. Electron diffraction was used to monitor the layer-by-layer growth. Films with 8, 14, and 20 monolayer- (ML) thick Co layers were investigated in situ by means of the magneto-optic Kerr effect. Characteristic hysteresis loops along the wedges, as a function of Cu thickness, unambiguously identify the oscillatory behavior in the sign of the exchange coupling between the two Co films. The oscillation periodicity (5.5 ML's of Cu) and, most importantly, the coupling strength are shown to be independent of the Co-layer thickness.