It is common for moral philosophers to reject a moral theory on the basis that its verdicts are unreasonably demanding—it requires too much of us to be a correct account of our moral obligations. Even though such objections frequently strike us as convincing, they give rise to two challenges: Are demandingness objections really independent of other objections to moral theories? Do standard demandingness objections not presuppose that costs borne by the comfortably off are more important than costs borne by the poor? These challenges have led some writers to question whether there really can be convincing demandingness objections, notwithstanding their strong initial appeal. David Sobel has argued that standard demandingness objections are ‘impotent’, Liam Murphy that they can be ‘dissolved’. In this paper, I aim to vindicate the possibility of demandingness objections by addressing these two challenges.