Ensemble methods in machine learning such as random forest, boosting, and bagging have been thoroughly studied and proven to have better accuracy than using a single predictor. However, their drawback is that they give models that can be much harder to interpret than those given by, for example, decision trees. In this work, we approach in a principled way the problem of constructing a decision tree that approximately reproduces a tree ensemble, exploring the tradeoff between accuracy and interpretability that can be obtained once exact reproduction is relaxed. First, we formally define the problem of obtaining the decision tree of a given depth that is most adherent to a tree ensemble and give a Dynamic Programming algorithm for solving this problem. We also prove that the decision trees obtained by this procedure satisfy generalization guarantees related to the generalization of the original tree ensembles, a crucial element for their effectiveness in practice. Since the computational complexity of the Dynamic Programming algorithm is exponential in the number of features, we also design heuristics to compute trees of a given depth with good adherence to a tree ensemble. Finally, we conduct a comprehensive computational evaluation of the algorithms proposed. The results indicate that in many situations, there is little or no loss in accuracy in working more interpretable classifiers: even restricting to only depth-6 decision trees, our algorithms produce trees with average accuracies that are within 1 percent (for the Dynamic Programming algorithm) or 2 percent (heuristics) of the original random forest.