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We examine the problem of evaluating selection queries over imprecisely represented objects. Such objects are used either because they are much smaller in size than the precise ones (e.g., compressed versions of time series), or as imprecise replicas of fast-changing objects across the network (e.g., interval approximations for time-varying sensor readings). It may be impossible to determine whether an imprecise object meets the selection predicate. Additionally, the objects appearing in the output are also imprecise. Retrieving the precise objects themselves (at additional cost) can be used to increase the quality of the reported answer. We allow queries to specify their own answer quality requirements. We show how the query evaluation system may do the minimal amount of work to meet these requirements. Our work presents two important contributions: first, by considering queries with set-based answers, rather than the approximate aggregate queries over numerical data examined in the literature; second, by aiming to minimize the combined cost of both data processing and probe operations in a single framework. Thus, we establish that the answer accuracy/performance tradeoff can be realized in a more general setting than previously seen.