Anonymous networks intended to enhance privacy and evade censorship are also being exploited for abusive activities. Technical schemes have been proposed to selectively revoke the anonymity of abusive users, or simply limit them from anonymously accessing online service providers. We designed an empirical survey study to assess the effects of deploying these schemes on 75 users of the Tor anonymous network. We evaluated proposed schemes based on examples of the intended or abusive use cases they may address, their technical implementation and the types of entities responsible for enforcing them. Our results show that revocable anonymity schemes would particularly deter the intended uses of anonymous networks. We found a lower reported decrease in usage for schemes addressing spam than those directly compromising free expression. However, participants were concerned that all technical mechanisms for addressing anonymous abuses could be exploited beyond their intended goals (51.7%) to harm users (43.8%). Participants were distrustful of the enforcing entities involved (43.8%) and concerned about being unable to verify (49.3%) how particular mechanisms were applied.