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Quorum-based protocols can be used to manage data when it is replicated at multiple server nodes to improve availability and performance. If some server nodes can be compromised by a malicious adversary, Byzantine quorums must be used to ensure correct access to replicated data. This paper introduces reconfigurable Byzantine quorums, which allow various quorum protocol parameters to be adapted based on the behavior of compromised nodes and the performance needs of the system. We present a protocol that generalizes dynamic Byzantine quorums by allowing the system size to change as faulty servers are removed from the system, in addition to adapting the fault threshold. A new architecture and algorithm that provide the capability to detect and remove faulty servers are also described. Finally, simulation results are presented that demonstrate the benefits offered by our approach.