Magnetic multilayer structures of Co/Cu prepared by dc magnetron sputtering are studied with respect to changing number of bilayers (N) for different thicknesses of the Cu spacer layer corresponding to different coupling conditions according to the oscillatory interlayer exchange coupling. X-ray reflectivity and diffuse scattering show that the multilayers become smoother with increasing N. The growth exponent of the roughness is found to be lower for a multilayer than for a single-layer film of similar thickness. The roughness of subsequent interfaces along the stack is conformal, and the lateral correlation does not change with the period number, but depends on the thickness of the spacer layers. The improved layer structure for larger N increases the antiferromagnetic coupling fraction as inferred from magneto-optic Kerr effect measurements and thereby increases the giant magnetoresistance (GMR) ratio up to 35% for N = 10. Thus, the first few bilayers do not contribute to the GMR but act as a buffer to improve the growth conditions for the following bilayers. The first about five bilayers can be replaced by a bottom Co layer of equivalent thickness which also improves the layer structure for a subsequently deposited lower number of bilayers without much loss in the GMR ratio. This smoothening effect due to the increasing of the thickness of the bottom-most layer is related to the simultaneously decreasing grain size.