We have investigated the influence of rotational excitation of the perturber molecule on the rate coefficient for vibrational relaxation of para-Hz. Comparison is made with our previous (quantum mechanical) calculations, which assumed the perturber molecule to be constrained to its rotational ground state, and with measurements of the rate coefficient. We also compare with the results of recent semi-classical calculations by Zenevich and Billing (Zenevich V A and Billing G D 1999 J. Chem. Phys. 111 2401).