Clinical journals increasingly illustrate uncertainty about the cost and effect of health care interventions using cost-effectiveness acceptability curves (CEACs). CEACs present the probability that each competing alternative is optimal for a range of values of the cost-effectiveness threshold. The objective of this article is to demonstrate the limitations of CEACs for presenting uncertainty in cost-effectiveness analyses. These limitations arise because the CEAC is unable to distinguish dramatically different joint distributions of incremental cost and effect. A CEAC is not sensitive to any change of the incremental joint distribution in the upper left and lower right quadrants of the cost-effectiveness plane; neither is it sensitive to radial shift of the incremental joint distribution in the upper right and lower left quadrants. As a result, CEACs are ambiguous to risk-averse policy makers, inhibit integration with risk attitude, hamper synthesis with other evidence or opinions, and are unhelpful to assess the need for more research. Moreover, CEACs may mislead policy makers and can incorrectly suggest medical importance. Both for guiding immediate decisions and for prioritizing future research, these considerable drawbacks of CEACs should make us rethink their use in communicating uncertainty. As opposed to CEACs, confidence and credible intervals do not conflate magnitude and precision of the net benefit of health care interventions. Therefore, they allow (in)formal synthesis of study results with risk attitude and other evidence or opinions. Presenting the value of information in addition to these intervals allows policy makers to evaluate the need for more empirical research.