We consider the problem of targeting benefits when the incomes of families are not accurately observable by the public authorities. By income uncertainty it is meant that the decision-maker cannot ascertain an applicant's income, but that he can assign probabilities with respect to the level of his resources. A decision-theoretic framework is used in order to analyze the decision to grant a benefit of fixed size. The derived decision rule consists of balancing the expected social cost of denying assistance to a person in need (type-I error) against that of granting a benefit to a non-poor (type-II error). Thus, when the cost of type-I errors are on the rise, or those of type-II errors fall, it becomes more desirable socially to increase population coverage of the benefit programme. Empirical illustrations are provided using a sample from the PSID.