The neutron slowing-down-time method for nondestructive assay of light water reactor spent fuel has been under development for many years. Results for a newly optimized design of a lead slowing-down-time spectrometer for spent-nuclear-fuel assay are presented. Monte Carlo analyses were performed to optimize the design of the assay device, determine its main parameters, investigate the effects of the spent-fuel assembly and the detector impurities on its performance, determine the fission signatures of the fissile isotopes in spent-fuel elements, and simulate the assay signal as a function of the slowing-down time, assuming threshold fission chambers for the assay detectors. The assay signals from the threshold detectors were analyzed to predict the unknown masses of the fissile isotopes in a typical spent commercial light water reactor fuel element. The broadened resolution of the system caused by the presence of the spent fuel inside the spectrometer pile was found sufficient to separate the signatures of the U and Pu fissiles in spent fuel.