Proof-of-work (PoW) is one of the most common techniques to defend against Sybil attacks. Unfortunately, current PoW defenses have two main drawbacks. First, they require work to be done even in the absence of an attack. Second, during an attack, they require good identities (IDs) to spend as much as the attacker. Recent theoretical work by Gupta, Saia, and Young suggests the possibility of overcoming these two drawbacks. In particular, they describe a new algorithm, GMCom, that always ensures that a minority of IDs are Sybil. They show that rate at which all good IDs perform computation is $O(J_G + \sqrt{T(J_G+1)})$, where $J_G$ is the join rate of good IDs, and $T$ is the rate at which the adversary performs computation. Unfortunately, this cost bound only holds in the case where (1) GMCom always knows the join rate of good IDs; and (2) there is a fixed constant amount of time that separates join events by good IDs. Here, we present ToGCom, which removes these two shortcomings. To do so, we design and analyze a mechanism for estimating the join rate of good IDs; and also devise a new method for setting the computational cost to join the system. Additionally, we evaluate the performance of ToGCom alongside prior PoW-based defenses. Based on our experiments, we design heuristics that further improve the performance of ToGCom by up to $3$ orders of magnitude over these previous Sybil defenses.