In the near future, as robots become more advanced and affordable, we can envision their use as intelligent assistants in a variety of domains. An exemplar human-robot task identified in many previous works is cooperatively carrying a physically large object. An important task objective is to keep the carried object level. In this work, we propose an admittance-based controller that maintains a level orientation of a cooperatively carried object. The controller raises or lowers its end of the object with a human-like behavior in response to perturbations in the height of the other end of the object (e.g., the end supported by the human user). We also propose a novel tuning procedure, and find that most users are in close agreement about preferring a slightly under-damped controller response, even though they vary in their preferences regarding the speed of the controller's response.