Boosted decision trees are among the most popular learning techniques in use today. While exhibiting fast speeds at test time, relatively slow training renders them impractical for applications with real-time learning requirements. We propose a principled approach to overcome this drawback. We prove a bound on the error of a decision stump given its preliminary error on a subset of the training data; the bound may be used to prune unpromising features early in the training process. We propose a fast training algorithm that exploits this bound, yielding speedups of an order of magnitude at no cost in the final performance of the classifier. Our method is not a new variant of Boosting; rather, it is used in conjunction with existing Boosting algorithms and other sampling methods to achieve even greater speedups.