Vibrational relaxation cross-sections and rate constants have been calculated for the deactivation of CO(v=1) by He-3 and He-4 on a new intermolecular potential with vibrational coordinate dependence [IT. G. A. Heijmen, R. Moszynski, P. E. S. Wormer and Ad van der Avoird, J. Chem. Phys. 107, 9921 (1997)]. The new surface is found to resolve the qualitative discrepancy between theory and experiment which existed in earlier theoretical calculations. The low impact energy regime has also been investigated focussing in particular on impact energies of less than 15 cm(-1) above the vibrational (v=1) threshold. Resonance structure has been found to occur and a comparison is made with an earlier investigation of the low temperature region. (C) 1997 American Institute of Physics. [S0021-9606(97)03246-7].