Left-to-right (LR) decoding (Watanabe et al., 2006) is promising decoding algorithm for hierarchical phrase-based translation (Hiero) that visits input spans in arbitrary order producing the output translation in left to right order. This leads to far fewer language model calls, but while LR decod- ing is more efficient than CKY decoding, it is unable to capture some hierarchical phrase alignments reachable using CKY decoding and suffers from lower transla- tion quality as a result. This paper in- troduces two improvements to LR decod- ing that make it comparable in translation quality to CKY-based Hiero.

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