A quantitative approach to optimizing computer systems requires a good understanding of how applications exercise a machine, and real program traces from production environments lead to the clearest understanding. Unfortunately, even the simplest program traces can leak sensitive details about users, their recent activity, or even details of trade secret algorithms. Given the cleverness of attackers working to undo well-intentioned, but ultimately insufficient, anonymization techniques, many organizations have simply decided to cease making traces available. Trace wringing is a new formulation of the problem of sharing traces where one knows a priori how much information the trace is leaking in the worst case. The key idea is to squeeze as much information as possible out of the trace without completely compromising its usefulness for optimization. We demonstrate the utility of a wrung trace through cache simulation and examine the sensitivity of wrung traces to a class of attacks on Advanced Encryption Standard (AES) encryption.