Most of the freely available parallel data to train the translation model of a statistical machine translation system comes from very specific sources (European parliament, United Nations, etc). Therefore, there is increasing interest in methods to perform an adaptation of the translation model. A popular approach is based on unsupervised training, also called self-enhancing. Both only use monolingual data to adapt the translation model. In this paper we extend the previous work and provide new insight in the existing methods. We report results on the translation between French and English. Improvements of up to 0.5 BLEU were observed with respect to a very competitive baseline trained on more than 280M words of human translated parallel data.