Given a scene consisting of objects, ray shooting queries answer with the first object encountered by a given ray, and are used in ray tracing and radiosity for rendering photo-realistic images in graphics, radio propagation simulation, and many other problems. We focus on one popular data structure for answering ray shooting queries—the octree. It is flexible and adaptive and has many applications. However, its degree of adaptiveness usually depends on manually selected parameters controlling its termination criteria. While practitioners usually rely on experience and heuristics, it is difficult to fix a set of parameter values that is good for all possible scenes. Recently, we introduced a simple cost predictor that reflects the average cost of ray shooting with a given octree (Cost prediction for ray shooting, in Proc. 18th Annu. ACM Sympos. Comput. Geom. (ACM, New York, 2002, pp. 293–302), and showed a termination criterion (cost-driven k-greedy) that guarantees a cost wit...