Norman Daniels' and James Sabin's theory of "accountability for reasonableness" (A4R) is a much discussed account of due process for decision-making on health care priority setting. Central to the theory is the acceptance that people may justifiably disagree on what reasons it is relevant to consider when priorities are made, but that there is a core set of reasons, that all centre on fairness, on which there will be no disagreement. A4R is designed as an institutional decision process which will ensure that only those reasons which everybody will agree are relevant and appropriate form part of decision-making. The argument which we will put forward in this paper questions whether it is a simple matter to delineate the core set of reasons and claims that it is a potential problem in A4R that it does not provide an indication of the exact content of this process. The paper first briefly outlines the content of A4R. It is argued that disagreement on what services should be high priorities cannot be resolved solely with a reference to "due process." In order to retain consistency over time, decision-makers are required to agree and articulate what reasons qualify as relevant and how conflicting reasons are to be balanced in the course of the process. The second and main part of the paper then considers how the reason of "solidarity" can be handled within the A4R framework, and it is shown that deciding whether solidarity should be admitted to the core set of allowable reasons is not a simple matter.