A variational method specially suited to neutron problems in small assemblies of coherent scatterers is described. The trial function used is a linear combination of a Maxwellian and exact solutions of the eigenvalue equation for two chosen values of buckling. This method accounts rather accurately for the sharp variations in the asymptotic neutron-energy spectrum (which arise because of discontinuities in the values of total scattering and transport cross sections) and also gives very accurate values for the fundamental mode-decay constant. As examples we have considered the decay of a neutron pulse in beryllium, beryllium oxide, and ice.