Using time-dependent high-resolution x-ray photoelectron spectroscopy at BESSY II, the adsorption and desorption processes of CO on stepped Pt(355) = Pt[5(111) x (111)] were investigated. From a quantitative analysis of C 1s data, the distribution of CO on the various adsorption sites can be determined continuously during adsorption and desorption. These unique data show that the terrace sites are only occupied when the step sites are almost saturated, even at temperatures as low as 130 K. The coverage-dependent occupation of on-top and bridge adsorption sites on the (111) terraces of Pt(355) is found to differ from that on Pt(111), which is attributed to the finite width of the terraces and changes in adsorbate-adsorbate interactions. In particular, no long-range order of the adsorbate layer could be observed by low-energy electron diffraction. Further details are derived from sticking coefficient measurements using the method devised by King and Wells [Proc. R. Soc. London, Ser. A 339, 245 (1974)] and temperature-programmed desorption. The CO saturation coverage is found to be slightly smaller on the stepped surface as compared to that on Pt(111). The initial sticking coefficient has the same high value of 0.91 for both surfaces.