Tree pattern queries (TPQs) provide a natural and easy formalism to query tree-structured XML data, and the efficient processing of such queries has attracted a lot of attention. Since the size of a TPQ is a key determinant of its evaluation cost, recent research has focused on the problem of query minimization using integrity constraints to eliminate redundant query nodes; specifically, TPQ minimization has been studied for the class of forward and subtype constraints (FT-constraints). In this paper, we explore the TPQ minimization problem further for a richer class of FBST-constraints that includes not only FT-constraints but also backward and sibling constraints. By exploiting the properties of minimal queries under FBST-constraints, we propose efficient algorithms to both compute a single minimal query as well as enumerate all minimal queries. In addition, we also develop more efficient minimization algorithms for the previously studied class of FT-constraints. Our experimental st...