Recent syntactic extensions of statistical translation models work with a synchronous context-free or tree-substitution grammar extracted from an automatically parsed parallel corpus. The decoders accompanying these extensions typically exceed quadratic time complexity. This paper extends the Direct Translation Model 2 (DTM2) with syntax while maintaining linear-time decoding. We employ a linear-time parsing algorithm based on an eager, incremental interpretation of Combinatory Categorial Grammar (CCG). As every input word is processed, the local parsing decisions resolve ambiguity eagerly, by selecting a single supertag–operator pair for extending the dependency parse incrementally. Alongside translation features extracted from the derived parse tree, we explore syntactic features extracted from the incremental derivation process. Our empirical experiments show that our model significantly outperforms the state-of-the art DTM2 system.