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Although integrity constraints have long been used to maintain data consistency, there are situations in which they may not be enforced or satisfied. In this paper, we present ConQuer, a system for efficient and scalable answering of SQL queries on databases that may violate a set of constraints. ConQuer permits users to postulate a set of key constraints together with their queries. The system rewrites the queries to retrieve all (and only) data that is consistent with respect to the constraints. The rewriting is into SQL, so the rewritten queries can be efficiently optimized and executed by commercial database systems.We study the overhead of resolving inconsistencies dynamically (at query time). In particular, we present a set of performance experiments that compare the efficiency of the rewriting strategies used by ConQuer. The experiments use queries taken from the TPC-H workload. We show that the overhead is not onerous, and the consistent query answers can often be computed within twice the time required to obtain the answers to the original (non-rewritten) query.