By use of circularly polarized synchrotron radiation at BESSY, spin-polarized photoemission from the valence orbitals of Xe and Kr atoms adsorbed on the Pt(111) single-crystal surface has been studied. Under certain conditions almost complete photoelectron polarization parallel or antiparallel to the photon spin was observed, allowing a direct assignment of quantum numbers of the states involved. Highly resolved intensity and polarization spectra in the threshold region exhibit pronounced variations versus photon energy.