This paper explores an inherent tension in modeling and querying uncertain data: simple, intuitive representations of uncertain data capture many application requirements, but these representations are generally incomplete―standard operations over the data may result in unrepresentable types of uncertainty. Complete models are theoretically attractive, but they can be nonintuitive and more complex than necessary for many applications. To address this tension, we propose a two-layer approach to managing uncertain data: an underlying logical model that is complete, and one or more working models that are easier to understand, visualize, and query, but may lose some information. We explore the space of incomplete working models, place several of them in a strict hierarchy based on expressive power, and study their closure properties. We describe how the two-layer approach is being used in our prototype DBMS for uncertain data, and we identify a number of interesting open problems to fully realize the approach.