Many large urban school districts match students to schools using algorithms that incorporate an element of random assignment. We introduce two simple empirical strategies to harness this randomization for value-added models (VAMs) measuring the causal effects of individual schools. The first estimator controls for the probability of being offered admission to different schools, treating the take-up decision as independent of potential outcomes. Randomness in school assignments is used to test this key conditional independence assumption. The second estimator exploits randomness in offers to generate instrumental variables (IVs) for school enrollment. This procedure uses a low-dimensional model of school quality mediators to solve the under- identification challenge arising from the fact that some schools are under-subscribed. Both approaches relax the assumptions of conventional value-added models while obviating the need for elaborate nonlinear estimators. In applications to data from Denver and New York City, we find that models controlling for both assignment risk and lagged achievement yield highly reliable VAM estimates. Estimates from models with fewer controls and older lagged score controls are improved markedly by IV.