Estimating the selectivity of queries is a crucial problem in database systems. Virtually all database systems rely on the use of selectivity estimates to choose amongst the many possible execution plans for a particular query. In terms of XML databases, the problem of selectivity estimation of queries presents new challenges: many evaluation operators are possible, such as simple navigation, structural joins, or twig joins, and many different indexes are possible ranging from traditional B-trees to complicated XML-specific graph indexes. A new synopsis for XML documents is introduced which can be effectively used to estimate the selectivity of complex path queries. The synopsis is based on a lossy compression of the document tree that underlies the XML document, and can be computed in one pass from the document. It has several advantages over existing approaches: (1) it allows one to estimate the selectivity of queries containing all XPath axes, including the order-sensitive ones, (2) the estimator returns a range within which the actual selectivity is guaranteed to lie, with the size of this range implicitly providing a confidence measure of the estimate, and (3) the synopsis can be incrementally updated to reflect changes in the XML database. 1