One of the major topics of political philosophy is that of distributive justice – the question of determining, as T. M. Scanlon famously named his book on the subject, what we owe to each other. The way this question is answered has huge effects on which policies should be pursued, and thus, how resources within and between societies are distributed. One important debate concerns which rule of distribution should govern distributive justice. Egalitarians argue that we should strive for equality as the distributive ideal. Others suggest sufficientarianism as the promising alternative, meaning that we should seek to bring people up to a certain well-being threshold. Recently, the sufficientarian view has been discussed quite heavily. Most notably, Casal has discussed and criticized the view very thoroughly in her article, Why Sufficiency Is Not Enough. Although her points of criticism are strong and well-constructed, we will argue that the sufficiency approach can be not only salvaged, but reconstructed and defended in a manner that affirms its strong candidacy for best answer to the political question of what we owe to each other. Our reconstructed sufficientarian account of distributive justice takes its starting point in duress as the relevant contrast to dignity. Human dignity, we define by expanding Kant’s notion of dignity as the moral worth of autonomous, rational persons to entail emotional valuable aspects of the human life and the praxis of embracing these aspects in a specifically human way. As the relevant contrast to dignity, duress is defined as a state of being in which a person is constrained in her opportunities for living without compromising her own humanity, either by failing to uphold central aspects of human life or by failing to enjoy these in a human way. Duress, therefore, captures the injustice of someone being below the level of a dignified human life to which they are entitled. Our reconstruction of the sufficientarian approach addresses the injustice of duress directly by suggesting a distributive scheme based on what we shall call frontiers of justice. This scheme suggests two separate thresholds, one of which relates to the moral importance of upholding people’s mere potential of a dignified human life (the potentiality frontier), the other to the actual attainment of human dignity (the dignity frontier). The advantage of such a reconstruction of the sufficientarian approach is twofold. Firstly, it accounts explicitly for the importance of giving morally founded reasons for applying a sufficientarian rule of distributive justice – an element that has traditionally been overseen by defenders of sufficientarianism. Secondly, it provides more plausible replies than alternative sufficiency standards to common objections to sufficientarianism.