A principal weakness of conventional (i.e., non-hierarchical) phrase-based statistical machine translation is that it can only exploit continuous phrases. In this paper, we extend phrase-based decoding to allow both source and target phrasal discontinuities, which provide better generalization on unseen data and yield significant improvements to a standard phrase-based system (Moses). More interestingly, our discontinuous phrasebased system also outperforms a state-of-the-art hierarchical system (Joshua) by a very significant margin (+1.03 BLEU on average on five ChineseEnglish NIST test sets), even though both Joshua and our system support discontinuous phrases. Since the key difference between these two systems is that ours is not hierarchical—i.e., our system uses a string-based decoder instead of CKY, and it imposes no hard hierarchical reordering constraints during training and decoding—this paper sets out to challenge the commonly held belief that the tree-based parameterization of systems such as Hiero and Joshua is crucial to their good performance against Moses.