Tree patterns represent important fragments of XPath. In this paper, we show that some classes of tree patterns exhibit such a property that, given a finite number of tree patterns P1, . . . , Pn, there exists another pattern P (tree pattern or DAG-pattern) such that P1, . . . , Pn are all contained in P, and for any tree pattern Q belonging to a given class C, P1, . . . , Pn are contained in Q implies P is contained in Q. Categories and Subject Descriptors H.2.4 [Query Processing]: Miscellaneous General Terms Theory, Algorithms Keywords XPath, Tree Pattern, Containment