The second-order energy shift in the Rayleigh-Schrrodinger perturbation theory is most likely to be positive for large quantum numbers, i.e. for excited states. Within the Wilson-Sommerfeld approximation, good for large quantum numbers, we show on the contrary that the sufficient condition for the second-order shift to be negative is, that the total potential be symmetric and both the unperturbed and perturbed potentials be monotonically increasing.