Calculations of the vibrational relaxation rate constants of the CO-He-3 and CO-He-4 systems are extended to lower temperatures than in any previous calculation and a comparison made with new experimental results in the temperature range 35-295 K for CO-He-3 and previously published results in the range 35-2300 K for CO-He-4. Both the coupled states (CS) and infinite-order sudden (IOS) approximations are used, with the self-consistent-held configuration interaction GO-He interaction potential of Diercksen and co-workers. The CS approximation is found to give a similar level of-agreement with experiment for the two isotopic species, while the performance of the IOS approximation is system dependent. The discrepancy between experimental and theoretical IOS rate constants is quite different for collisions involving He-3 and He-4, so that it is not profitable to compare IOS results directly with experiment for these two systems at temperatures below 300 K. The differences between the measured and the CS calculated rate constants for both the CO-He-4 and CO-He-3 systems are thought to be due predominantly to inaccuracies in the interaction potential. Relaxation rate constants for CO target molecules in collision with HD, D-2 and H-2 are compared with results involving He-3, He-4, and "He-2," revealing some systematic trends depending only on mass. However, for all hydrogen species there are marked upturns in the rate constants at low temperatures relative to those for helium atoms, while the rate constants for HD are greater than those for He-3 throughout the temperature range. Calculations at small initial kinetic energies for the CO-He systems reveal an unexpected increase in relaxation cross section with reduction in kinetic energy. This implies that at very low temperatures the CO-He rate constants will show an upturn with decreasing temperature. The fact that this effect is smaller than that for the CO-hydrogen systems and occurs at lower temperatures is consistent with the shallower CO-He attractive well compared with that for CO-H-2.