In this paper, we dissect the influence of several target-side dependency-based extensions to hierarchical machine translation, including a dependency language model (LM). We pursue a non-restrictive approach that does not prohibit the production of hypotheses with malformed dependency structures. Since many questions remained open from previous and related work, we offer in-depth analysis of the influence of the language model order, the impact of dependencybased restrictions on the search space, and the information to be gained from dependency tree building during decoding. The application of a non-restrictive approach together with an integrated dependency LM scoring is a novel contribution which yields significant improvements for two large-scale translation tasks for the language pairs Chinese–English and German–French.