The selection of appropriate epithermal group-averaged cross sections for use in a few-group criticality calculation is particularly difficult when resonance absorbers are present. However, by use of the SOFOCATE code for the calculation of thermal spectra in hydrogenous media, it is now practical to include low-lying resonances below 2 ev in the thermal group. Since the SOFOCATE code, which is based on the Wigner-Wilkins differential equation for monatomic hydrogen thermalization, has yielded good agreement with measured spectra in water, it is felt that use of this code and inclusion of low-lying resonances in the thermal group constitute a more accurate and convenient method of treating these resonances than other procedures. As an application of the method, a study has been made of some of the effects associated with the use of Eu as a means of reducing the temperature defect in water-moderated reactors. It is shown that the use of natural, unshielded Eu would reduce the temperature defect provided the spectral hardening introduced by the core absorption is sufficiently small. It is also shown that the strong dependence on spectral hardening is due to the presence of the Eu resonances at about 0.4 ev.