The statistical treatment of the proton model for hydrogen absorption by palladium is extended to include a variation of the electron donation energy with hydrogen content, as determined by a density of states function for the combined 4d- and 5s-bands for palladium. This improved model gives better agreement with the high pressure limiting solubility data and the observed critical composition than the original model, when both are fitted to the critical isotherm by the same method. An apparent anomaly in the variation of the isosteric enthalpy of absorption with content is explained by the improved model.