The density-of-states function of individual colloidal PbSe nanocrystals varying in diameter between 3 and 7 nm is measured by resonant tunneling spectroscopy. It is in semiquantitative agreement with tight-binding calculations, but the energy separation between electron (hole) levels of S and P symmetry is systematically smaller than predicted by the theory. These results provide an explanation for the second and third excitonic optical transitions, which have been debated for a long time.