State of the art Tree Structures Prediction techniques rely on bottom-up decoding. These approaches allow the use of context-free features and bottom-up features. We discuss the limitations of mainstream techniques in solving common Natural Language Processing tasks. Then we devise a new framework that goes beyond Bottom-up Decoding, and that allows a better integration of contextual features. Furthermore we design a system that addresses these issues and we test it on Hierarchical Machine Translation, a well known tree structure prediction problem. The structure of the proposed system allows the incorporation of non-bottom-up features and relies on a more sophisticated decoding approach. We show that the proposed approach can find better translations using a smaller portion of the search space.