Many fault-tolerant systems rely on overprovisioning of system resources to provide spare capacity that can compensate for faulty components. However, this approach often results in idle resources that would be otherwise unnecessary; these resources do not provide an effective contribution to the system functionality but they may adversely affect its performance (as in the case of unused replicas that take part in distributed protocols, generating more messages than would be necessary). In this paper we introduce a mechanism for reconfiguring an overlay network topology in Byzantine settings. Our protocols use backup nodes to replace failed ones while ensuring that a replacement node is able to join the network with a prescribed connectivity. We show that topology reconfiguration is a powerful mechanism that can be used for building intrusion-tolerant distributed systems.