We consider the problem of optimizing conjunctive queries in the presence of inclusion and functional dependencies. We show that the problem of containment (and hence those of equivalence and non-minimality) is in NP when either (a) there are no functional dependencies or (b) the set of dependencies is what we call key-bused. These results assume that infinite databases are allowed. If only finife databases are allowed, new containments may arise, as we illustrate by an example. We also prove a

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... "compactness" theorem that shows that no such examples can exist for case (b).