Richard Arneson has proposed that prioritarianism be adjusted to incorporate considerations of individual desert. For those inclined to accept prioritarianism, this refinement seems intuitive: Shouldn't we give priority both to those who are worse off and to those at a higher desert level? This article considers the viability of desert-modulated prioritarianism using the framework of claims-across-outcomes (‘claims’). I have previously used this framework to provide a unified defence of the Pareto and Pigou–Dalton axioms. With further, plausible, axioms, we arrive at prioritarianism. Should the strength of an individual's claim depend upon her desert? If so, we should accept a new axiom, Priority for the More Deserving. But Priority for the More Deserving can conflict with the Pareto axioms, if desert is intrapersonally variable rather than fixed. We should therefore reject Priority for the More Deserving and conclude that desert-modulated prioritarianism is a non-starter.