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This paper presents novel approaches to reordering in phrase-based statistical machine translation. We perform consistent reordering of source sentences in training and estimate a statistical translation model. Using this model, we follow a phrase-based monotonic machine translation approach, for which we develop an efficient and flexible reordering framework that allows to easily introduce different reordering constraints. In translation, we apply source sentence reordering on word level and use a reordering automaton as input. We show how to compute reordering automata on-demand using IBM or ITG constraints, and also introduce two new types of reordering constraints. We further add weights to the reordering automata. We present detailed experimental results and show that reordering significantly improves translation quality.