We describe a method for selecting optimal actions affecting the sensors in a probabilistic state estimation framework, with an application in selecting optimal zoom levels for a motor-controlled camera in an object tracking task. The action is selected to minimize the expected entropy of the state estimate. The contribution of this paper is the ability to incorporate varying costs into the action selection process by looking multiple steps into the future. The optimal action sequence then minimizes both the expected entropy and the costs it incurs. This method is then tested with an object tracking simulation, showing the benefits of multi-step versus single-step action selection in cases where the cameras’ zoom control motor is insufficiently fast.