Numerous works in Statistical Machine Translation (SMT) have attempted to identify better translation hypotheses obtained by an initial decoding using an improved, but more costly scoring function. In this work, we introduce an approach that takes the hypotheses produced by a state-ofthe-art, reranked phrase-based SMT system, and explores new parts of the search space by applying rewriting rules selected on the basis of posterior phraselevel confidence. In the medical domain, we obtain a 1.9 BLEU improvement over a reranked baseline exploiting the same scoring function, corresponding to a 5.4 BLEU improvement over the original Moses baseline. We show that if an indication of which phrases require rewriting is provided, our automatic rewriting procedure yields an additional improvement of 1.5 BLEU. Various analyses, including a manual error analysis, further illustrate the good performance and potential for improvement of our approach in spite of its simplicity.