This paper considers the practical problem of distributing a fixed budget for poverty alleviation to a population whose poverty status is not directly observable. The solution we propose improves on the techniques that are commonly used in practice by taking both the concavity of the social welfare function and the entire conditional distribution of poverty status into account, and by endogenously determining the optimal transfer levels. We provide an algorithm to calculate the optimal transfers for any population of benefit applicants. Finally, we explain how our method is a generalization of statistical classification techniques and thus provide an intuitive discussion of the defects of currently operational methods.