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 im(cid:173) portant subproblem - identifying phrase structure. The first is a Marko(cid:173) vian approach that extends standard HMMs to allow the use of a rich ob(cid:173) servation structure and of general classifiers to model state-observation dependencies. The second is an extension of constraint satisfaction for(cid:173) malisms. We develop efficient combination algorithms under both mod(cid:173) els and study them experimentally in the context of shallow parsing.