Debates on how to reduce poverty and inequality have focused on two controversial questions: Should social policies be targeted to low-income groups or be universal? Should benefits be equal for all or earnings-related? Traditional arguments in favor of targeting and flat-rate benefits, focusing on the distribution of the money actually transferred, neglect three policy-relevant considerations: (1) The size of redistributive budgets is not fixed but reflects the structure of welfare state institutions. (2) A trade-off exists between the degree of low-income targeting and the size of redistributive budgets. (3) Outcomes of market-based distribution are often more unequal than those of earnings-related social insurance programs. We argue that social insurance institutions are of central importance for redistributive outcomes. Using new data, our comparative analyses of the effects of different institutional types of welfare states on poverty and inequality indicate that institutional differences lead to unexpected outcomes and generate the paradox of redistribution: The more we target benefits at the poor and the more concerned we are with creating equality via equal public transfers to all, the less likely we are to reduce poverty and inequality.