It is demonstrated that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially by supersymmetry. A hierarchy of approximate supersymmetric potentials is obtained which allows one to calculate the energies of higher rovibrational states from the energies of lower rovibrational states for which Pekeris' expression is accurate. This new formulation is tested by calculating the energies of rovibrational states of the hydrogen molecule and comparing the results with those of accurate numerical calculations. (C) 2004 Elsevier B.V. All rights reserved.