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It is well known that statistical machine translation systems perform best when they are adapted to the task. In this paper we propose new methods to quickly perform incremental adaptation without the need to obtain word-by-word alignments from GIZA or similar tools. The main idea is to use an automatic translation as pivot to infer alignments between the source sentence and the reference translation, or user correction. We compared our approach to the standard method to perform incremental re-training. We achieve similar results in the BLEU score using less computational resources. Fast retraining is particularly interesting when we want to almost instantly integrate user feed-back, for instance in a post-editing context or machine translation assisted CAT tool. We also explore several methods to combine the translation models.