We present a method for improving word alignment quality for phrase-based statistical machine translation by reordering the source text according to the target word order suggested by an initial word alignment. The reordered text is used to create a second word alignment which can be an improvement of the first alignment, since the word order is more similar. The method requires no other pre-processing such as part-of-speech tagging or parsing. We report improved Bleu scores for English-to-German and English-to-Swedish translation. We also examined the effect on word alignment quality and found that the reordering method increased recall while lowering precision, which partly can explain the improved Bleu scores. A manual evaluation of the translation output was also performed to understand what effect our reordering method has on the translation system. We found that where the system employing reordering differed from the baseline in terms of having more words, or a different word order, this generally led to an improvement in translation quality.