Colloidal semiconductor quantum dots (QDs) are attractive materials for realizing highly flexible, solution-processable optical gain media, but they are difficult to use in lasing because of complications associated with extremely short optical-gain lifetimes limited by nonradiative Auger recombination. By combining compositional grading of the QD's interior for hindering Auger decay with postsynthetic charging for suppressing parasitic ground-state absorption, we can reduce the lasing threshold to values below the single-exciton-per-dot limit. As a favorable departure from traditional multi-exciton-based lasing schemes, our approach should facilitate the development of solution-processable lasing devices and thereby help to extend the reach of lasing technologies into areas not accessible with traditional, epitaxially grown semiconductor materials.