Targeting is a core element of anti-poverty program design, with benefits typically targeted to those most “deprived" in some sense (e.g., consumption, wealth). A large literature in economics examines how to best identify these households feasibly at scale, usually via proxy means tests (PMTs). We ask a different question, namely, whether targeting the most deprived has the greatest social welfare benefit: in particular, are the most deprived those with the largest treatment effects or do the “poorest of the poor" sometimes lack the circumstances and complementary inputs or skills to take full advantage of assistance? We explore this potential trade-off in the context of an NGO cash transfer program in Kenya, utilizing recent advances in machine learning (ML) methods (specifically, generalized random forests) to learn PMTs that target both a) deprivation and b) high conditional average treatment effects across several policy-relevant outcomes. We found that targeting solely on the basis of deprivation is generally not attractive in a social welfare sense, even when the social planner's preferences are highly redistributive. We show that a planner using simpler prediction models, based on OLS or less sophisticated ML approaches, could reach divergent conclusions. We discuss implications for the design of real-world anti-poverty programs at scale.