The pressure broadening and shifting coefficients for pure rotational transitions of CO in a He bath gas at very low temperatures are calculated from the best available potential energy surfaces, and compared with very recent measurements by M. M. Beaky, T. M. Goyette, and F. C. De Lucia [J. Chem. Phys. 105, 3994 (1996)]. The results obtained for two recent empirical potentials determined from fits to Van der Waals spectra, and for a recent high quality purely ab initio surface, are consistent with one another. The best of the spectroscopic potentials also yields good agreement with high temperature virial coefficients and transport properties. Predictions from all three of these potentials agree with linebroadening and shifting measurements at temperatures above similar to 20 K, but are in substantial disagreement with the measurements at temperatures below 4 K. At present, the source of this discrepancy is not known.