We introduce a broad family of decision trees, Composite Trees, whose leaf classifiers are selected out of a hypothesis set composed of p subfamilies with different complexities. We prove new data-dependent learning guarantees for this family in the multi-class setting. These learning bounds provide a quantitative guidance for the choice of the hypotheses at each leaf. Remarkably, they depend on the Rademacher complexities of the sub-families of the predictors and the fraction of sample points correctly classified at each leaf. We further introduce random composite trees and derive learning guarantees for random composite trees which also apply to Random Forests. Using our theoretical analysis, we devise a new algorithm, RANDOMCOMPOSITEFORESTS (RCF), that is based on forming an ensemble of random composite trees. We report the results of experiments demonstrating that RCF yields significant performance improvements over both Random Forests and a variant of RCF in several tasks.