This paper reviews and discusses cost-effectiveness acceptability curves as a basis for prioritising investments in safety measures in the offshore oil and gas industry. We conclude that such curves should be used with caution, as cost-effectiveness acceptability curves focus mainly on the probability that safety measures are cost-effective. Consequently, safety measures with a small probability of being cost-effective, but with a potential of being highly cost-effective in actual demand situations, could then be given low priority compared to other safety measures. To improve the basis for prioritising safety measures, we recommend including assessments of the cost-effectiveness given an actual demand situation, in addition to the probability that the safety measure is cost-effective. We also highlight the importance of reflecting the strength of knowledge on which the probability and the cost-effectiveness assignments are based.