In this paper we show that the priority search tree of McCreight, which was originally developed to satisfy a class of spatial search queries on 2-dimensional points, can be adapted to the problem of dynamically maintaining a set of keys so that the query complexity adapts to the distribution of queried keys. Presently, the best-known example of such a data structure is the splay tree, which dynamically reconfigures itself during each query so that frequently accessed keys move to the top of the tree and thus can be retrieved with fewer queries than keys that are lower in the tree. However, while the splay tree is conjectured to offer optimal adaptive amortized query complexity, it may require O(n) for individual queries. We show that an access-adaptive priority search tree (AAPST) can provide competitive adaptive query performance while ensuring O(log n) worst-case query performance, thus potentially making it more suitable for certain interactive (e.g.,online and real-time) applications for which the response time must be bounded.