We derive the scattering amplitude N (r) for a QCD dipole on a dense target in the semi-classical approximation. We include the first subleading correction in the target thickness arising from similar to rho(4) operators in the effective action for the large-x valence charges. Our result for N (r) can be matched to a phenomenological proton fit by Albacete et al. over a broad range of dipole sizes r and provides a definite prediction for the A-dependence for heavy-ion targets. We find a suppression of N (r) for finite A for dipole sizes a few times smaller than the inverse saturation scale, corresponding to a suppression of the classical bremsstrahlung tail. (C) 2012 Elsevier B.V. All rights reserved.