Recent observations on VV transfer in H-2 have shown interesting results. For nonresonant processes, comparison of the experimental rate constants with the results of previous semiclassical calculations, quantum oscillators/classical rotors coupled via classical collisions, showed the theoretical rate constants to be too slow by a factor of 3 or more. The semiclassical rate constant of the resonant VV process (v = 1 + v = 0 -> v = 0 + v = 1) was also found to be too slow, by more than an order of magnitude, compared with the experimental rate. Further, the semiclassical model predicted the value of k(1,1 -> 0,2) to exceed that of k(1,0 -> 0,1), but the experimental data shows it to be a factor of approximately 2 less. In this work we employ an accurate interaction potential for the H-2-H-2 system, and treat both rotation and vibration of the diatoms as coupled quantum-mechanical degrees of freedom. These new calculated results are in better overall agreement with the near-resonant experimental values, but the calculated rate constants are a factor of 2 to 3 larger than experiment for the nonresonant processes