While in solids the phonon-assisted, non-radiative decay from high-energy excited states to lowenergy excited states is picosecond fast, it was hoped that electron and hole relaxation could be slowed down in quantum dots, due to the unavailability of phonons energy-matched to the large energy-level spacings ("phonon-bottleneck"). However, excited-state relaxation was observed to be rather fast (≤ 1 ps) in InP, CdSe, and ZnO dots, and explained by an efficient Auger mechanism, whereby the excess energy of electrons is transferred non-radiatively to holes, which can then decay rapidly by phonon emission, by virtue of the densely spaced valence-band levels. The recent emergence of PbSe as a novel quantum-dot material has rekindled the hope for a slow-down of excited-state relaxation, because hole relaxation was deemed to be ineffective on account of the widely spaced hole levels. The assumption of sparse hole energy levels in PbSe was based on an effective-mass argument based on the light effective mass of the hole. Surprisingly, fast intraband relaxation times of 1 to 7 ps were observed in PbSe quantum dots, and have been considered contradictory with the Auger cooling mechanism, because of the assumed sparsity of the hole energy levels. Our pseudopotential calculations, however, do not support the scenario of sparse hole levels in PbSe: Because of the existence of three valence-band maxima in the bulk PbSe band structure, hole energy levels are densely spaced, in contradiction with simple effective-mass models. The remaining question is whether the Auger decay channel is sufficiently fast to account for the fast intraband relaxation. Using the atomistic pseudopotential wave functions of Pb2046Se2117 and Pb260Se249 quantum-dots, we calculated explicitly the electron-hole Coulomb integrals and the P→S electron Auger relaxation rate. We find that the Auger mechanism can explain the experimentally observed P→S intraband decay time scale without the need to invoke any exotic relaxation mechanisms.PACS numbers: