An improved version of a recently reported semiclassical wavepacket approach is used to compute initial state selected total integral cross sections as well as thermal rate constants for the reaction OH+H-2 --> H2O+H. The method involves treating the diatomic vibrations as well as their relative translational motion quantum mechanically by solving the time-dependent Schrodinger equation. The rotational motion is described classically. The computed initial state selected total reaction cross section and rate constants are in satisfactory agreement with the recently reported six-dimensional wavepacket results of Zhang and Zhang. Computed thermal rate constants are in good agreement with the six-dimensional quantal results of Manthe et al. but roughly a factor of three higher than the experimental results at 300 K.