In previous works, we have introduced an alternative perturbation scheme to find approximate solutions of the spectral problem for the rotation-vibration molecular Hamiltonian. An important feature of our approach is that the zero order Hamiltonian is the direct product of a purely vibrational Hamiltonian with the identity on the rotational degrees of freedom. The convergence of our method for the methane vibrational ground state was very satisfactory and our predictions were quantitative. In the present article, we provide further details on the implementation of the method in the degenerate and quasi-degenerate cases. The quasi-degenerate version of the method is tested on excited polyads of methane, and the results are assessed with respect to a variational treatment. The optimal choice of the size of quasi-degenerate spaces is determined by a trade-off between speed of convergence of the perturbation series and the computational effort to obtain the effective super-Hamiltonian.