Oxidation of CO over size-selected Ptn clusters (n = 1, 2, 4, 7, 10, 14, 18) supported on alumina thin films grown on Re(0001) was studied using temperature-programmed reaction/desorption (TPR/TPD), X-ray and ultraviolet photoelectron spectroscopy (XPS/UPS), and low energy ion scattering spectroscopy (ISS). The activity of the model catalysts was found to vary by a factor of five with deposited Ptn size during the first reaction cycle (TPR) and by a factor of two during subsequent cycles, with Pt2 being the least active and Pt14 the most active. The limiting step in the reaction appears to be the binding of oxygen; however, this does not appear to be an activated process as reaction is equally efficient for 300 K and 180 K oxidation temperatures. Size-dependent shifts in the valence band onset energy correlate strongly with CO oxidation activity, and there is also an apparent correlation with the availability of a particular binding site, as probed by CO TPD. The morphology of the clusters also becomes more three dimensional over the same size range, but with a distinctly different size-dependence. The results suggest that both electronic structure and the availability of particular binding sites control activity.