We describe a synchronous parsing algorithm that is based on two successive monolingual parses of an input sentence pair. Although the worst-case complexity of this algorithm is and must be O(n 6 ) for binary SCFGs, its average-case run-time is far better. We demonstrate that for a number of common synchronous parsing problems, the two-parse algorithm substantially outperforms alternative synchronous parsing strategies, making it efficient enough to be utilized without resorting to a pruned search.