Rare diseases pose a particular priority setting problem. The UK gives rare diseases special priority in healthcare priority setting. Effectively, the National Health Service is willing to pay much more to gain a quality-adjusted life-year related to a very rare disease than one related to a more common condition. But should rare diseases receive priority in the allocation of scarce healthcare resources? This article develops and evaluates four arguments in favour of such a priority. These pertain to public values, luck (...) egalitarian distributive justice the epistemic difficulties of obtaining knowledge about rare diseases and the incentives created by a higher willingness to pay. The first is at odds with our knowledge regarding popular opinion. The three other arguments may provide a reason to fund rare diseases generously. However, they are either overinclusive because they would also justify funding for many non-rare diseases or underinclusive in the sense of justifying priority for only some rare diseases. The arguments thus fail to provide a justification that tracks rareness as such. There are no data in this work. (shrink)