Abstract--Until quite recently, extending Phrase-based Statistical Machine Translation (PBSMT) with syntactic knowledge caused system performance to deteriorate. The most recent successful enrichments of PBSMT with hierarchical structure either employ non-linguistically motivated syntax for capturing hierarchical reordering phenomena, or extend the phrase translation table with redundantly ambiguous syntactic structures over phrase pairs. In this work we present an extended, harmonised account of our previous work which showed that incorporating linguistically motivated lexical syntactic descriptions, called supertags, can yield significantly better PBSMT systems at insignificant extra computational cost. We describe a novel PBSMT model that integrates supertags into the target language model and the target side of the translation model. Two kinds of supertags are employed: those from Lexicalized TreeAdjoining Grammar and Combinatory Categorial Grammar. Despite the differences between ...