We study both empirically and theoretically the consequences of introducing a conditional cash transfer scheme for the distribution of program impacts. Intuitively, if the conditioned-on good is normal, then better-offhouseholds tend to receive a larger positive impact. I formalize this insight by means of a simple model of child labor, applying the Nash-Bargaining approach as the solution concept. A series of tests for heterogeneity in program impacts are developed and applied to Progresa, an anti-poverty program in Mexico. It can be concluded that this program exhibits a lot of heterogeneity in treatment effects. Consistent with the model, and under the assumption of rank preservation, program impacts are distributionally regressive, although positive, within the treated population