This paper as exemplified by the Millennium Declaration of the United Nations, the reduction of poverty and hunger are now seen as central objectives of international development. Yet the modalities for attaining these goals are contested. Further, while it might be assumed that interventions that alleviate poverty will automatically reduce hunger, a number of studies of the relationship between income and the acquisition of food suggest that this assumption may be incorrect. There are sharply divergent views as to how much narrowly targeted interventions actually benefit the poor. These result from differing assessments of three issues: whether better targeting outcomes are likely to be achieved, whether such methods are cost-effective, and whether the living standards of the poor are improved by such targeted interventions. This paper contributes to this debate through an analysis of a Mexican antipoverty program called PROGRESA (the Programa de Educación, Salud y Alimentación). PROGRESA provides cash transfers linked to children's enrollment and regular school attendance and to clinic attendance. By 2000, it reached approximately 2.6 million families, about 40 percent of all rural families and about one-ninth of all families in Mexico. We use a longitudinal sample of approximately 24,000 households from 506 communities.... We find that the impact is greatest on dietary quality as measured by the acquisition of calories from vegetable and animal products -- a finding consistent with the view of respondents themselves that PROGRESA was enabling them to to eat better.