Pressure broadening and line shift parameters for the 1-0 and 2-1 rotational transitions of carbon monoxide in collision with helium have been measured between 1 and 600 K. Measurements below 30 K were made using the collisional cooling technique, while measurements at higher temperatures were made in an equilibrium cell. The experimental apparatus and techniques employed in the study are described. Pressure broadening and line shift cross sections are compared with theoretical predictions based on the best available potential energy surface, and differences between theoretical predictions and the experimental results are discussed. Potential sources of systematic experimental error are examined as a possible origin of these differences.