The generalized search tree, or GiST, defines the basic interfaces required to construct a hierarchical access method for database systems. As originally specified, GiSTs only support record selection. In this paper, we show how a small number of additional interfaces enable GiSTs to support a much larger class of search and computation operations. Members of this class, which includes nearest-neighbor and ranked search, user-defined aggregation and index-assisted selectivity estimation, are increasingly common in new database applications. The advantages of implementing these operations in the GiST framework include reduction of user development effort and the ability to use "industrial strength" concurrency and recovery mechanisms provided by expert implementors.