The electronic structure of Pd clusters deposited on polycrystalline graphite has been investigated by x-ray photoemission, Auger spectroscopy, and bremsstrahlung isochromat spectroscopy. Initial- and final-state shifts of energy levels as a function of the average cluster size R are small, but important modifications of the density of filled and empty states at the Fermi level are observed. With decreasing particle size, the d portion of the conduction band broadens and shifts to higher energy while its valence counterpart shows the opposite shift. A simple analytical model is developed which accounts in some detail for the measured shifts and linewidths and also explains earlier x-ray-absorption data. The size dependences are explained in terms of mixing of Pd 4d and graphite * continua with a squared coupling constant V2 proportional to R-1. As a consequence a gap opens up across the Fermi level in the cluster density of states and unoccupied hybrid resonances arise as observed experimentally. Initial-state energy shifts and cluster charging are estimated and found to play a minor role for the present system.