The interplay between non-local phenomena during growth and the evolution of interfacial roughness was investigated in Co/Cu multilayers grown by rf-magnetron sputtering. In particular, we compared samples where the presence of correlated interfacial roughness, namely interface undulations, is more or less pronounced by changing the underlayer or the multilayer stacking. We performed anomalous grazing incidence measurements to observe how the vertical correlation length, xi(perpendicular to), changes as a function of the in-plane length scale of the roughness. L. xi(perpendicular to) is expected to monotonically decrease with L. but we found that xi(perpendicular to) displays a maximum for specific L values featuring a high degree of in-plane correlation. This effect seems to be related with the features of the multilayer stacking. (C) 2012 Elsevier B.V. All rights reserved.