We present detailed investigations on the optical properties of PbSe nanocrystals. The absorption spectra of monodisperse, quasispherical nanocrystals exhibit sharp features as a result of distinct optical transitions. To study the size dependence, absorption spectra of nanocrystals ranging from 3.4 to 10.9 nm in diameter are analysed and a total of 11 distinct optical transitions are identified. The assignment of the various optical transitions is discussed and compared to theoretically calculated transition energies. By plotting all transitions as a function of nanocrystal size (D) we find that the energy (E) changes with the following relationship [Formula: see text] for the lowest energy transitions. The transition energy extrapolates to approximately 0.3 eV for infinite crystal size, in agreement with the bandgap of bulk PbSe at the L-point in the Brillouin zone. In addition, high-energy transitions are observed, which extrapolate to 1.6 eV for infinite crystal size, which is in good agreement with the bulk bandgap of PbSe at the Sigma-point in the Brillouin zone. Tight-binding calculations confirm that the high-energy transitions originate from the Sigma-point in the Brillouin zone. The Sigma-character of the high-energy transitions may be of importance to explain the mechanism behind multiple exciton generation in PbSe nanocrystals.