We address the problem of training the free parameters of a statistical machine translation system. We show significant improvements over a state-of-the-art minimum error rate training baseline on a large ChineseEnglish translation task. We present novel training criteria based on maximum likelihood estimation and expected loss computation. Additionally, we compare the maximum a-posteriori decision rule and the minimum Bayes risk decision rule. We show that, not only from a theoretical point of view but also in terms of translation quality, the minimum Bayes risk decision rule is preferable.