We study the problem of combining the outcomes of several different classifiers in a way that provides a coherent inference that satisfies some constraints. In particular, we develop two general approaches for an important subproblem - identifying phrase structure. The first is a Markovian approach that extends standard HMMs to allow the use of a rich observation structure and of general classifiers to model state-observation dependencies. The second is an extension of constraint satisfaction formalisms. We develop efficient combination algorithms under both models and study them experimentally in the context of shallow parsing.