Multidimensional indices have been successfully introduced to the field of querying on XML data. Using R*-tree, T. Grust proposed an interesting method to support all XPath axes. In that method, each node of an XML document is labeled with a five-dimensional descriptor. All the nodes of the XML document are mapped to a point set in a five-dimensional space. T. Grust made it clear that each of the XPath axes can be implemented by a range query in the above five-dimensional space. Thus, R*-tree can be used to improve the query performance for XPath axes. However, according to our investigations, most of the range queries for the XPath axes are partially-dimensional range queries. That is, the number of query dimensions in each of the range queries is less than five, although the R*-tree is built in the five-dimensional space. If the existing multidimensional indices are used for such range queries, then a great deal of information that is irrelevant to the queries also has to be read from disk. Based on this observation, a new multidimensional index structure (called Adaptive R*-tree) is proposed in this paper to support the XPath axes more efficiently.