This paper proposes a new methodology for estimating teacher value-added. Rather than imposing a normality assumption on unobserved teacher quality (as in the standard empirical Bayes approach), our nonparametric estimator permits the underlying distribution to be estimated directly and in a computationally feasible way. The resulting estimates fit the unobserved distribution very well regardless of the form it takes, as we show in Monte Carlo simulations. Implementing the nonparametric approach in practice using two separate large-scale administrative data sets, we find the estimated teacher value-added distributions depart from normality and differ from each other. To draw out the policy implications of our method, we first consider a widely-discussed policy to release teachers at the bottom of the value-added distribution, comparing predicted test score gains under our nonparametric approach with those using parametric empirical Bayes. Here the parametric method predicts similar policy gains in one data set while overestimating those in the other by a substantial margin. We also show the predicted gains from teacher retention policies can be underestimated significantly based on the parametric method. In general, the results highlight the benefit of our nonparametric empirical Bayes approach, given that the unobserved distribution of value-added is likely to be context-specific. [Additional support for this research was provided by the University of Toronto Mississauga.]