We propose a method to overcome Auger recombination in nanocrystal quantum dot lasers using cavity-enhanced spontaneous emission. We derive a numerical model for a laser composed of nanocrystal quantum dots coupled to optical nanocavities with small mode-volume. Using this model, we demonstrate that spontaneous emission enhancement of the biexciton transition lowers the lasing threshold by reducing the effect of Auger recombination. We analyze a photonic crystal nanobeam cavity laser as a realistic device structure that implements the proposed approach. (C) 2014 Optical Society of America