This paper presents a new kind of problem in the ethics of distribution. The problem takes the form of several 'calibration dilemmas', in which intuitively reasonable aversion to small-stakes inequalities requires leading theories of distribution to recommend intuitively unreasonable aversion to large-stakes inequalities. We first lay out a series of such dilemmas for prioritarian theories. We then consider a widely endorsed family of egalitarian views and show that they are subject to even more forceful calibration dilemmas than prioritarian theories. Finally, we show that our results challenge common utilitarian accounts of the badness of inequalities in resources.