The inelastic moderation of fast neutrons in heavy moderators can be described by a simple model giving the mean energy loss of neutrons upon leaving a scattering system, as a function of the mean number of collisions undergone, . Experiments with several neutron sources (Ra-Be, D-D, D-T) are in accordance with a nearly linear dependence, () as a suitable phenomenological description. The mean energies were determined by means of measurement of the neutron migration areas in a large moderating water volume surrounding spherical lead and bismuth scatterers. The consistency of our results has been checked by comparison with predictions of the evaporation model of inelastic scattering.