The Single Introduction (S.I.) method for the measurement by hydrogen chemisorption of metal dispersion in supported metal catalysts has been tested on two commercial 5% Pd/Al2O3 catalysts. The S.I. results are compared with those obtained by the classical method of determining the adsorption isotherm (i.e., the multiple introduction method) and by O2/H-2 titration. As in Part I of this work, both chemisorption and thermal desorption have been used to find the best experimental conditions for the "Back-Sorption" procedure. It is shown that alpha- and beta-palladium hydrides can be decomposed by outgassing the samples for less then 5 min at 305 K and 10(-6) Torr and that 30 min pumping at the same temperature and pressure is sufficient to eliminate from the catalyst surface the weakly adsorbed hydrogen as well. It has also been verified that chemisorption of hydrogen on these catalysts at room temperature is complete at pressures lower than those required for the alpha --> beta phase transition, so that it is possible to perform dispersion measurements by means of a simple S.I. of hydrogen coupled with Back-Sorption below 15 Torr at 305 K. Temperature-programmed desorption of hydrogen on one of the samples outlines the need to discriminate among the different adsorbed species for a more detailed characterization of supported metal catalysts.