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This paper describes a lexical trigger model for statistical machine translation. We present various methods using triplets incorporating long-distance dependencies that can go beyond the local context of phrases or n-gram based language models. We evaluate the presented methods on two translation tasks in a reranking framework and compare it to the related IBM model 1. We show slightly improved translation quality in terms of BLEU and TER and address various constraints to speed up the training based on Expectation-Maximization and to lower the overall number of triplets without loss in translation performance.