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A lease is a token which grants its owner exclusive access to a resource for a defined span of time. In order to be able to tolerate failures, leases need to be coordinated by distributed processes. We present FaTLease, an algorithm for fault-tolerant lease negotiation in distributed systems. It is built on the Paxos algorithm for distributed consensus, but avoids Paxos' main performance bottleneck of requiring persistent state. This property makes our algorithm particularly useful for applications that can not dispense any disk bandwidth. Our experiments show that FaTLease scales up to tens of thousands of concurrent leases and can negotiate thousands of leases per second in both LAN and WAN environments.