This paper analyzes the optimal allocation of a given antipoverty budget consistent with various usual measures of poverty. It is shown that it is generally optimal to give all the budget either to the poorest or to the richest of the poor. It is only with the Sen index of poverty that it is sometimes optimal to combine both types of allocation. This property may be related to the normalization rule used in the derivation of that measure and sheds some new light on the axiomatics of poverty measurement.
