When considering the introduction of a new intervention in a budget constrained healthcare system, priority setting based on fair principles is fundamental. In many jurisdictions, a multi-criteria approach with several different considerations is employed, including severity and cost-effectiveness. Such multi-criteria approaches raise questions about how to balance different considerations against each other, and how to understand the logical or normative relations between them. For example, some jurisdictions make explicit reference to a large patient benefit as such a consideration. However, since patient benefit is part of a cost-effectiveness assessment it is not clear how to balance considerations of greater patient benefit against considerations of severity and cost-effectiveness. The aim of this paper is to explore the role of a large patient benefit as an independent criterion for priority setting in a healthcare system also considering severity and cost-effectiveness. By taking the opportunity cost of new interventions (i.e., the health forgone in patients already receiving treatment) into account, we argue that patient benefit has a complex relationship to priority setting. More specifically, it cannot be reasonably concluded that large patient benefits should be given priority if severity, cost-effectiveness, and opportunity costs are held constant. Since we cannot find general support for taking patient benefit into account as an independent criterion from any of the most discussed theories about distributive justice: utilitarianism, prioritarianism, telic egalitarianism and sufficientarianism, it is reasonable to avoid doing so. Hence, given the complexity of the role of patient benefit, we conclude that in priority practice, a large patient benefit should not be considered as an independent criterion, on top of considerations of severity and cost-effectiveness.