The single-particle self-energy in finite nuclei is constructed in a microscopic way by means of the Green-function formalism. We present calculations for the 208Pb system which are fully self-consistent up to second order in the residual interaction. This leads to an improved description of damping effects in the spectral function for deeply bound hole states. The theoretical results are compared with experimental (e, e'p) results. Global properties of the single-particle strength distributions for deep hole states, such as the centroids and widths, are well reproduced. Finally some comments are made about the meaning of occupation probabilities for shell-model orbits.