The surface of Pt clusters with average size between 1 and 8 nm supported on SiO2, gamma-Al2O3 or Y-zeolite was probed by Xe-129 NMR as the Pt surface coverage with hydrogen, theta, was increased. A distinct change in the structure of the hydrogen overlayer at theta almost-equal-to 0.3 was inferred from. the NMR spectra. This change is believed to take place when the chemisorbed hydrogen fills all the next nearest neighbor metal sites and the nearest neighbors start to be occupied. These new observations clarify previously reported determinations of the average number of Pt atoms in supported clusters by means of Xe NMR and other techniques. It also appears that interfacial metal-support interactions may be probed by Xe NMR.