The authors investigate the binding energy separation between the many-body ground-state singlet and higher-lying magnetic states for the f¹-f² Anderson model to next-leading order in the 1/N expansion, where N denotes the orbital degeneracy of the f states. They formulate integral equations for the magnetic-state amplitudes that appear at next-leading order in 1/N and solve these, together with the integral equations that describe the singlet, numerically. They find that the total separation between magnetic and singlet states is small, even in the valence-fluctuation regime, and hence demonstrate the robustness of the leading-order result. They find that the maximum binding-energy separation is shifted towards higher valence, in contradiction to results of the minimal-degeneracy model. They also present results for the valence and charge susceptibility.