Korpi and Palme's (1998) classic "The Paradox of Redistribution and Strategies of Equality" claims that universal social policy better reduces poverty than social policies targeted at the poor. This article revisits Korpi and Palme's classic, and in the process, explores and informs a set of enduring questions about social policy, politics, and social equality. Specifically, we investigate the relationships between three dimensions of welfare transfers - "transfer share" (the average share of household income from welfare transfers), low-income targeting, and universalism - and poverty and preferences for redistribution. We analyze rich democracies like Korpi and Palme, but also generalize to a broader sample of developed and developing countries. Consistent with Korpi and Palme, we show: a) poverty is negatively associated with the transfer share and universalism; b) redistribution preferences are negatively associated with low-income targeting; and c) universalism is positively associated with the transfer share. Contrary to Korpi and Palme, redistribution preferences are not related to transfer share or universalism; and low-income targeting is not positively associated with poverty and not negatively associated with transfer share. Therefore, instead of the "paradox of redistribution" we propose two new paradoxes of social policy: noncomplementarity and undermining. The non-complementarity paradox is that there is a mismatch between the dimensions that matter to poverty and the dimension that matters to redistribution preferences. The undermining paradox emphasizes that the dimension (transfer share) that most reduces poverty tends to increase with the one dimension (low-income targeting) that reduces support for redistribution.