We present a scheme for exact collision detection between complex models undergoing rigid motion and deformation. The scheme relies on a hierarchical model representation using axis-aligned bounding boxes (AABBs). In recent work, AABB trees have been shown to be slower than oriented bounding box (OBB) trees. In this paper, we describe a way to speed up overlap tests between AABBs, such that for collision detection of rigid models, the difference in performance between the two representations is greatly reduced. Furthermore, we show how to quickly update an AABB tree as a model is deformed. We thus find AABB trees to be the method of choice for collision detection of complex models undergoing deformation. In fact, because they are not much slower to test, are faster to build, and use less storage than OBB trees, AABB trees might be a reasonable choice for rigid models as well.