This paper studies boosting algorithms that make a single pass over a set of base classifiers. We first analyze a one-pass algorithm in the setting of boosting with diverse base classifiers. Our guarantee is the same as the best proved for any boosting algorithm, but our one-pass algorithm is much faster than previous approaches. We next exhibit a random source of examples for which a ``picky'' variant of AdaBoost that skips poor base classifiers can outperform the standard AdaBoost algorithm, which uses every base classifier, by an exponential factor. Experiments with Reuters and synthetic data show that one-pass boosting can substantially improve on the accuracy of Naive Bayes, and that picky boosting can sometimes lead to a further improvement in accuracy.