The thermoelectric properties of the layered oxides KxRhO2 (x = 1/2 and 7/8) are investigated by means of the electronic structure, as determined by ab inito calculations and Boltzmann transport theory. In general, the electronic structure of KxRhO2 is similar to NaxCoO2, but with strongly enhanced transport. K7/8RhO2 exceeds the ultrahigh power factor of Na0.88CoO2 reported previously by more than 50%. The roles of the cation concentration and the lattice parameters in the transport properties in this class of compounds are explained.