Deprivations normally give rise to undeserved inequality. It is commonly thoughtthat one way of improving a situation with respect to equality is by reducing the incidence ofdeprivations. In this paper I argue that there is at least one respect in which reducing theincidence of deprivations can make things worse from the point of view of equality. Whileeliminating deprivations leads to the elimination of inequalities, reducing the incidence ofdeprivations leads to an uneven distribution of the pairwise relations of inequality of apopulation, which leads to the concentration of pairwise relations of inequality in the worseoff. If my argument is correct, egalitarians have reasons to broaden their dimensions ofconcern: egalitarians should not only be concerned about the unequal distribution of goods,but also about the unequal distribution of pairwise relations of inequality of a population.