The ADtree, a data structure useful for caching sufficient statistics, has been successfully adapted to grow lazily when memory is limited and to update sequentially with an incrementally updated dataset. However, even these modified forms of the ADtree still exhibit inefficiencies in terms of both space usage and query time, particularly on datasets with very high dimensionality and with high arity features. We propose five modifications to the ADtree, each of which can be used to improve size and query time under specific types of datasets and features. These modifications also provide an increased ability to precisely control how an ADtree is built and to tune its size given external memory or speed requirements.