To evaluate the potential of the lead slowing-down-time spectrometer quantitatively as a nuclear safeguards assay device, the time-, space-, &nd energy-dependent neutron diffusion equation has been solved for heavy moderators, and a FORTRAN-iV program, SLAHM (Slowlng-Down Analysis in heavy Moderators), was written to perform the required Integrations.Using this new calculational tool, spectral and spatial distributions have been obtained at a variety of times following introduction of a 14-MeV point source of neutrons into several different-sized lead assemblies. One can apparently achieve a 235 U/ 239 Pu discrimination ratio >5 with only limited self-shielding (even for high enrichment fuels) by examining the energy regions from 2.8 to 3.8 and 56 to 100 eV or, for highly enriched ylutonium breeder fuel, 2.8 ':o 3.8 and 56 to 66 eV. Note that this technique requires a 2-m cube. Further, the neutron population for energies below the inelastic threshold based upon exponencial attenuation (e~B T) involving the neutron age (T cm 2 ) must be estimated very carefully. The "true" age has been shown to be sensitive to both cross-section variation and the "free ride" affoided by the (n,2n) interaction.