This paper considers the problem of active object recognition using touch only. The focus is on adaptively selecting a sequence of wrist poses that achieves accurate recognition by enclosure grasps. It seeks to minimize the number of touches and maximize recognition confidence. The actions are formulated as wrist poses relative to each other, making the algorithm independent of absolute workspace coordinates. The optimal sequence is approximated by Monte Carlo tree search. We demonstrate results in a physics engine and on a real robot. In the physics engine, most object instances were recognized in at most 16 grasps. On a real robot, our method recognized objects in 2--9 grasps and outperformed a greedy baseline.