Small palladium clusters, produced by vapour deposition onto amorphous carbon substrates, were analysed in situ by photoelectron spectroscopy (XPS, UPS) and characterized ex situ by transmission electron microscopy. These combined measurements provide the actual cluster size dependence of the two well-known effects in the photoelectron spectra of small supported clusters - the valence band narrowing and the core-electron binding energy shift - suggesting the following explanations: the valence band narrowing is due to an initial state effect, while the core-level shift is dominated by the effect of the changed final state, as it is predicted by Wertheim et al.