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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 dependency-based 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.