Standard phrase-based translation models do not explicitly model context dependence between translation units. As a result, they rely on large phrase pairs and target language models to recover contextual effects in translation. In this work, we explore n-gram models over Minimal Translation Units (MTUs) to explicitly capture contextual dependencies across phrase boundaries in the channel model. As there is no single best direction in which contextual information should flow, we explore multiple decomposition structures as well as dynamic bidirectional decomposition. The resulting models are evaluated in an intrinsic task of lexical selection for MT as well as a full MT system, through n-best reranking. These experiments demonstrate that additional contextual modeling does indeed benefit a phrase-based system and that the direction of conditioning is important. Integrating multiple conditioning orders provides consistent benefit, and the most important directions differ by language pair.