The additional effects of the Coriolis anti-pairing (CAP) and blocking on the second-order rotational-vibrational (RV) Hamiltonian are discussed for even nuclei. This leads to lower limits on the pairing correlation energy W0 and the critical spin Ic introduced by Mottelson and Valatin. Typical lower limits deduced from available experimental data are W0 = 2–3 MeV and Ic = 24(OS186) and 50(U238). The blocking constant τ deduced from experiment is in agreement with the theoretical estimate. This analysis also suggests that, in going from the lowest to the highest spins so far obtained in ground state bands, a smooth transition is to be expected from the superconducting to the rigid moments of inertia with a function dependence and magnitude similar to that obtained from a careful treatment of the rotation-vibration interaction.