Though there is much work on how inconsistency in databases should be managed, there is good reason to believe that end users will want to bring their domain expertise and needs to bear in how to deal with inconsistencies. In this paper, we propose the concept of Inconsistency Management Policies (IMPs). We show that IMPs are rich enough to specify many types of inconsistency management methods proposed previously, but provide end users with tools that allow them to use the policies that they want. Our policies are also capable of allowing inconsistency to persist in the database or of eliminating more than a minimal subset of tuples involved in the inconsistency. We present a formal axiomatic definition of IMPs and present appropriate complexity results, together with results linking different IMPs together. We extend the relational algebra (RA) to incorporate IMPs and present theoretical results showing how IMPs and classical RA operators interact.