The challenges associated with poverty measurement using a cardinal variable have received much attention over the past four decades, but there is a dearth of literature on how to meaningfully assess poverty with an ordinal variable. This article proposes a class of simple, intuitive, and policy-relevant poverty measures for ordinal variables. The measures are sensitive to the depth of deprivations, unlike the headcount ratio. Moreover, under appropriate restrictions, the measures ensure that priority is given to the poorest among the poor when targeting, monitoring, and evaluating poverty alleviation programs. To assess the robustness of poverty comparisons to alternative choices of parameters, the article develops various stochastic dominance tests (some of which are novel contributions to the stochastic dominance literature). The empirical illustration documenting changes in sanitation deprivation in Bangladesh showcases the measures' ability to identify instances in which overall sanitation deprivation improved while leaving the poorest behind.