This paper presents a novel numerical scheme applicable to the solution of the Boltzmann transport equation by means of a spherical-harmonics expansion. This scheme improves the solution at low energies, keeping the desired accuracy in the calculation of the mean quantities while saving a significant amount of CPU time. This is important in view of the applications of the method, since the typical number of nodes to be used in the combined space-energy domain is in the range of 104–105.