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Certain answers are a principled method for coping with uncertainty that arises in many practical data management tasks. Unfortunately, this method is expensive and may exclude useful (if uncertain) answers. Thus, users frequently resort to less principled approaches to resolve the uncertainty. In this paper, we propose Uncertainty Annotated Databases (UA-DBs), which combine an underand over-approximation of certain answers to achieve the reliability of certain answers, with the performance of a classical database system. Furthermore, in contrast to prior work on certain answers, UA-DBs achieve a higher utility by including some (explicitly marked) answers that are not certain. UA-DBs are based on incomplete K-relations, which we introduce to generalize the classical set-based notions of incomplete databases and certain answers to a much larger class of data models. Using an implementation of our approach, we demonstrate experimentally that it efficiently produces tight approximations of certain answers that are of high utility.