The narrow resonance (NR) approximation has, in the past, been applied mainly to regular lattices with fairly simple unit cells. Attempts to use the NR approximation to deal with fine details of the lattice structure, or with complicated lattice cells, have generally been based on assumptions and approximations that are rather difficult to evaluate. A benchmark method is developed in which slowing down is still treated in the NR approximation, but spatial neutron transport is handled by Monte Carlo. This benchmark method is used to evaluate older methods for analyzing the doubleheterogeneity effect in fast reactors, and for computing resonance integrals in the PROTEUS lattices. New methods for treating the PROTEUS lattices are proposed.