In many real-world scenarios, we must make judgments in the presence of computational constraints. One common computational constraint arises when the features used to make a judgment each have differing acquisition costs, but there is a fixed total budget for a set of judgments. Particularly when there are a large number of classifications that must be made in a real-time, an intelligent strategy for optimizing accuracy versus computational costs is essential. E-mail classification is an area where accurate and timely results require such a trade-off. We identify two scenarios where intelligent feature acquisition can improve classifier performance. In granular classification we seek to classify e-mails with increasingly specific labels structured in a hierarchy, where each level of the hierarchy requires a different trade-off between cost and accuracy. In load-sensitive classification, we classify a set of instances within an arbitrary total budget for acquiring features. Our method, Adaptive Classifier Cascades (ACC), designs a policy to combine a series of base classifiers with increasing computational costs given a desired trade-off between cost and accuracy. Using this method, we learn a relationship between feature costs and label hierarchies, for granular classification and cost budgets, for load-sensitive classification. We evaluate our method on real-world e-mail datasets with realistic estimates of feature acquisition cost, and we demonstrate superior results when compared to baseline classifiers that do not have a granular, cost-sensitive feature acquisition policy.