Social programmes for poverty alleviation involve eligibility rules and transfer rules that often proxy-means tests. We propose to specify the estimator in connection with the poverty alleviation problem. Three distinct stages emerge from the optimization analysis: the identification of the poor, the ranking of their priorities and the calculus of the optimal transfer amount. These stages are implemented simultaneous by using diverse distribution regression methods to generate fitted-values of living standards plugged into the poverty minimization programme to obtain the transfer amounts. We apply these methods to Egypt in 2013. Recentered Influence Function (RIF) regressions focusing on the poor correspond to the most efficient transfer scheme. Most of the efficiency gain is obtained by making transfer amounts varying across beneficiaries rather than by varying estimation methods. Using RIF regressions instead of quantile regressions delivers only marginal poverty alleviation, although it allows for substantial reduction of the exclusion of the poor.