Many distributed systems are subject to the Sybil attack, where an adversary subverts system operation by emulating behavior of multiple distinct nodes. Most recent work to address this problem leverages social networks to establish trust relationships between users. However, the use of social networks is not appropriate in all systems, as they can be subverted by social engineering techniques, require nodes in a P2P network to maintain and be aware of social network information, and may require overly optimistic assumptions about the fast-mixing nature of social links. This paper explores an alternate approach. We present SybilControl, a novel, decentralized scheme for controlling the extent of Sybil attacks. SybilControl is an admission control mechanism for nodes in a distributed system that requires them to periodically solve computational puzzles. SybilControl consists of a distributed protocol to allow nodes to collectively verify the computational work of other nodes, and mechanisms to prevent the malicious influence of misbehaving nodes that do not perform the computational work. We investigate the practical issues involved with deploying SybilControl into existing DHTs, particularly with resilient lookup protocols. We evaluate SybilControl through simulations and find that SybilControl retains low overhead and latency. Additionally, even when the adversary controls 20% of the system's computational resources, SybilControl-enabled DHTs can be configured to maintain lookup performance at over 99% success rate using low communication overhead.