In this paper an improved degenerate kernel is obtained and subsequently used instead of the exact thermalization kernel for the calculation of thermal-neutron densities in a heterogeneous reactor lattice.The degenerate kernel is composed of a number of functions, some of which are obtained by conserving speed moments of the kernel while the remaining functions are chosen so as to reproduce scattering probabilities involving epithermal energies. The degenerate kernel satisfies the detailed balance strictly and, as opposed to conventional degenerate kernels, shows the desirable feature of improved accuracy when the number of terms in the degenerate kernel is increased.This degenerate kernel is employed to compute thermal-neutron spectra in cylindricized unit cells by solving the integral transport equation for the scalar neutron density. For this purpose the DESMOS code was developed. The results of these calculations are compared with the analogous THERMOS code results. DESMOS proves to be accurate and its speed of execution compares favorably with that of THERMOS.