We consider the problem of targeting benefits when the decision-maker cannot ascertain an applicant's income, but can assign probabilities with respect to the level of his resources. A decision-theoretic framework is used to analyze the decision to grant a benefit of fixed size. The proposed rule consists in balancing the expected social cost of denying assistance to the needy (type-I error) against that of granting a benefit to a non-poor (type-II error). Thus, when the costs of type-I errors are on the rise, or those of type-II errors fall, it becomes more desirable to increase population coverage of the programme.