Norman Daniels' theory of justice and health faces a serious practical problem: his theory can ground the special moral importance of health and allows distinguishing just from unjust health inequalities, but it provides little practical guidance for allocating resources when they are especially scarce. Daniels' solution to this problem is a fair process that he specifies as "accountability for reasonableness". Daniels claims that accountability for reasonableness makes limit-setting decisions in healthcare not only legitimate, but also fair. This paper assesses the latter claim. Does accountability for reasonableness result in fair limit-setting decisions? It is argued that the answer to this question is not a clear yes. Daniels is remarkably unclear about the criterion of fairness that accountability for reasonableness satisfies. The paper discusses different options for resolving this lack of clarity and examines how they apply to Daniels' accountability for reasonableness framework. It is concluded, first, that accountability for reasonableness is not a paradigm case of any of the classic notions of procedural justice; second, that what might be called "constrained pure procedural justice" best reflects how accountability for reasonableness results in fair limit-setting decisions; and third, that the procedural conditions of accountability for reasonableness must be further specified and amended to better achieve a fair process, and hence fair limit-setting decisions.