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Despite the widespread and growing use of asynchronous copies to improve scalability, performance and availability, this practice still lacks a firm semantic foundation. Applications are written with some understanding of which queries can use data that is not entirely current and which copies are "good enough"; however, there are neither explicit requirements nor guarantees. We propose to make this knowledge available to the DBMS through explicit currency and consistency (C&C) constraints in queries and develop techniques so the DBMS can guarantee that the constraints are satisfied. In this paper we describe our model for expressing C&C constraints, define their semantics, and propose SQL syntax. We explain how C&C constraints are enforced in MTCache, our prototype mid-tier database cache, including how constraints and replica update policies are elegantly integrated into the cost-based query optimizer. Consistency constraints are enforced at compile time while currency constraints are enforced at run time by dynamic plans that check the currency of each local replica before use and select sub-plans accordingly. This approach makes optimal use of the cache DBMS while at the same time guaranteeing that applications always get data that is "good enough" for their purpose.