Size-dependent effects in the core-peak and Fermi-edge features of Au-cluster photoemission spectra have been investigated for two different substrates: polycrystalline and highly oriented pyrolytic graphite. In contrast with common substrates such as amorphous carbon, graphite or silicon dioxide, for pyrolitic graphite it has been found that steps or cavities bind the clusters, that assume non-spherical shapes. The use of pyrolitic graphite in our experiments, therefore, enabled us to investigate clusters with asymmetrical shape, in which the electron-hole final-state interaction observed for spheric clusters should be greatly reduced. We show that the spectral energy shifts with changing coverage detected for such clusters cannot be explained with a final-state mechanism alone - and indicate that initial-state as well as final-state effects are present for the Au 4f core peaks.