XML document markup is highly repetitive and therefore well com-pressible using dictionary-based methods such as DAGs or gram-mars. In the context of selectivity estimation, grammar-compressed trees were used before as synopsis for structural XPath queries. Here a fully-fledged index over such grammars is presented. The index allows to execute arbitrary tree algorithms with a slow-down that is comparable to the space improvement. More interestingly, certain algorithms execute much faster over the index (because no decompression occurs). E.g., for structural XPath count queries, evaluating over the index is faster than previous XPath implemen-tations, often by two orders of magnitude. The index also allows to serialize XML results (including texts) faster than previous sys-tems, by a factor of ca. 2–3. This is due to efficient copy han-dling of grammar repetitions, and because materialization is totally avoided. In order to compare with twig join implementations, we implemented a materializer which writes out pre-order numbers of result nodes, and show its competitiveness. 1.