A single-colour three-photon ionisation technique has been employed to identify some high-lying odd levels of uranium I in the region 34000-43000 cm^-1. Details of the transition identifications of observed resonances, made by a comparison with the optogalvanic spectra and taking into account different possible routes to ionisation, are discussed. The data suggest that sequential two-step excitation or near-resonant two-photon excitation is a prerequisite for single-colour photoionisation resonance to show up above background.