The local adsorption geometries of the (2 2)-1O, (2 2)-2O, (2 2)-(O + CO) and (2 2)-(O + 2CO) phases on the Rh(111) surface have been investigated by analysing low-energy electron diffraction (LEED) intensity data. In all cases, the oxygen atoms were found to occupy the threefold fcc site and the topmost layer spacing d 1 2 of Rh(111) was found to be expanded by about 3%. Additional experiments with disordered oxygen overlayers prepared at low adsorption temperatures show a monotonic increase of d 1 2 with oxygen coverage. An O coverage of θ 0 0.1 already lifts the contraction of 0.02 of the clean surface. This finding is remarkable as for Ru(0001) a substantial expansion of the first layer spacing ( 3%) is observed only at very high O coverages, e.g. for the (1 1)-O structure. For the high-coverage Rh(111)-(2 2)-2O phase a honeycomb arrangement of the O atoms can clearly be ruled out. The (2 2)-2O has rather to be regarded as a (2 1)-1O phase. In the mixed (2 2)-(O + CO) overlayer the CO molecule occupies the on-top position which is also expected from a reduced back-donation of (substrate) electron charge density due to coadsorbed O atoms. The presence of CO molecules weakens the Rh-O bond. Altogether, the structural findings nicely reflect the competition of CO and O for electron charge density at the Rh(111) surface. In the (2 2)-(O + 2CO) phase 60% of available hcp sites and 100% of available on-top sites in the (2 2) unit cell are occupied.