Abstract: Public officials often impose eligibility requirements that have two effects: (1) they screen out ineligible people and (2) they screen out eligible people. Consisting of paperwork of administrative burdens, such requirements are sometimes characterized as “sludge,” and for some eligible people, they might prove overwhelming or prohibitive. In these circumstances, there is a pervasive normative issue: what is the optimal tradeoff between (1) and (2)? It is plausible to think that a great deal depends on numbers. If, for example, the number of ineligible people who are screened out is very large, and if the number of eligible people who are screened out is very small, then there would seem little ground for objection. But if the number of eligible people who are screened out is very large, there is a serious problem, and it might be worthwhile to consider an approach that would not screen out eligible people, even if it would simultaneously fail to screen out, or effectively “screen in,” a small number of ineligible people. We identify competing, plausible positions on the normative question, which we label consequentialist and legalist. We also offer the results of a pilot study, which shows that the overwhelming majority of respondents would favor changes that allow ineligible people to receive benefits, if that is the price of ensuring that eligible people do so as well – unless the number of ineligible recipients is very high. The survey results suggest that most people reject the legalist position and embrace a form of consequentialism.