Programs using means tests to identify low-income households face a trade-off between promoting access and ensuring program integrity. The authors use a comparison-district design to estimate the effects of a pilot program to improve the accuracy of the process of certifying students for free or reduced-price meals in the National School Lunch Program. This pilot program required households to provide income documentation with their applications for these benefits. Requiring income documentation did not reduce the proportion of ineligible households getting free or reduced-price meals. Furthermore, this requirement did reduce access to the program among eligible households. (Contains 3 tables, 3 figures, and 14 notes.)