We present new ensemble learning algorithms for multi-class classification. Our algorithms can use as a base classifier set a family of deep decision trees or other rich or complex families and yet benefit from strong generalization guarantees. We give new data-dependent learning bounds for convex ensembles in the multi-class classification setting expressed in terms of the Rademacher complexities of the sub-families composing the base classifier set, and the mixture weight assigned to each sub-family. These bounds are finer than existing ones both thanks to an improved dependency on the number of classes and, more crucially, by virtue of a more favorable complexity term expressed as an average of the Rademacher complexities based on the ensemble’s mixture weights. We introduce and discuss several new multi-class ensemble algorithms benefiting from these guarantees, prove positive results for the H-consistency of several of them, and report the results of experiments showing that their performance compares favorably with that of multi-class versions of AdaBoost and Logistic Regression and their L1-regularized counterparts.