The need for intelligent interaction of a robot with its environment frequently requires sensing of the environment. Further, the need for rapid execution requires that the interaction between sensing and action take place using as little sensory data as possible, while still being reliable. Previous work has developed a technique for rapidly determining the feasible poses of an object from sparse, noisy, occluded sensory data. In this paper, we examine techniques for acquiring position and surface orientation data about points on the surfaces of objects, with the intent of selecting sensory points that will force a unique interpretation of the pose of the object with as few data points as possible. Under some simple assumptions about the sensing geometry, we derive a technique for predicting optimal sensing positions. The technique has been implemented and tested. To fully specify the algorithm, we need estimates of the error in estimating the position and orientation of the object, and we derive analytic expressions for such error for the case of one particular approach to object recognition.