We have shown theoretically that efficient multiple-exciton generation (MEG) by a single photon can be observed in small nanocrystals. Our quantum simulations that include hundreds of thousands of exciton and multiexciton states demonstrate that the complex time-dependent dynamics of these states in a closed electronic system yields a saturated MEG effect on a picosecond time scale. Including phonon relaxation confirms that efficient MEG requires the exciton-biexciton coupling time to be faster than exciton relaxation time.