Using grants programs to induce poor parents to send their children to school has received considerable attention as an instrument to break the inheritance of poverty. Yet, the cost of these programs tends to be quite high so that increasing their efficiency is an important issue that needs to be researched. We use the educational component of Progresa in Mexico to explore alternative targeting and calibrating schemes to achieve this purpose. We show that targeting on risk of non-enrollment instead of targeting on poverty, as currently done, would be implementable and create huge efficiency gains. To start with, this would concentrate grants on secondary school since attendance to primary school is virtually universal, saving 55% of the educational budget. Targeting the population most likely to drop out of school upon completing primary and allowing for variable transfers across beneficiaries would result in a 72% efficiency gain for that cohort over targeting on poverty and making uniform transfers by gender, reducing leakage cost from 85% to 53% of the budget. Even restricting transfers to be uniform across beneficiaries but set at the optimal level would achieve a 65% efficiency gain. However, to make the scheme easy to implement, only observable, transparent, and non-manipulable indicators of risk should be used and discrete levels of transfers offered. This would still result in a 53% efficiency gain over the current scheme.