The effective integration of MT technology into computer-assisted translation tools is a challenging topic both for academic research and the translation industry. Particularly, professional translators feel crucial the ability of MT systems to adapt to their feedback. In this paper, we propose an adaptation scheme to tune a statistical MT system to a translation project using small amounts of post-edited texts, like those generated by a single user in even just one day of work. The same scheme can be applied at the larger scale in order to focus general purpose models towards the specific domain of interest. We assess our method on two domains, namely information technology and legal, and four translation directions, from English to French, Italian, Spanish and German. The main outcome is that our adaptation strategy can be very effective provided that the seed data used for adaptation is enough related to the remaining text to translate; otherwise, MT quality does neither improve nor worsen, thus showing the robustness of our method.