Standard parameter estimation schemes for statistical translation models can struggle to find reasonable settings on some parallel corpora. We show how auxiliary information can be used to constrain the procedure directly by restricting the set of alignments explored during parameter estimation. This enables the integration of bilingual and monolingual knowledge sources while retaining the flexibility of the underlying models. We demonstrate the effectiveness of this approach for incorporating linguistic and domain-specific constraints on various parallel corpora, and consider the importance of using the context of the parallel text to guide the application of such constraints.