Many ethical theorists believe that a given distribution of healthcare is morally justified only if (1) it is cost-effective and (2) it does not discriminate against older adults and disabled people. However, if (3) cost-effectiveness involves maximizing the number of quality-adjusted life-years (QALYs) added by a given unit of healthcare resource, or cost, it seems the pursuit of cost-effectiveness will inevitably discriminate against older adults and disabled patients. I show why this trilemma is harder to escape than some theorists think. We cannot avoid it by using age- or disability-weighted QALY scores, for example. I then explain why there is no sense of discrimination on which discrimination is both unjust, and thus something healthcare rationing must avoid, and something cost-effective healthcare rationing inevitably involves. I go on to argue that many of the reasons we have for not favoring rationing that maximizes QALYs outside the healthcare context apply in healthcare as well. Thus, claim (1) above is dubious.