Hierarchies are frequently used for the organization of objects. Given a hierarchy of classes, two main approaches are used, to automatically classify new instances: flat classification and cascade classification. Flat classification ignores the hierarchy, while cascade classification greedily traverses the hierarchy from the root to the predicted leaf. In this paper we propose a new approach, which extends cascade classification to predict the right leaf by estimating the probability of each root-to-leaf path. We provide experimental results which indicate that, using the same classification algorithm, one can achieve better results with our approach, compared to the traditional flat and cascade classifications.