I think the best way is to have your own Bitcoin exchange. This is why exchanges are under the radar of AML law.
I don't think that's a good idea because you have track everything because of these KYC/AML laws.
Some of the best option are in operating your own (onion) mixer service which is being well-established and trusted. In this case you have full control of the log files created by your own service. If I were a mixer operator which is taking it's own medicine, I would also keep logs for troubleshooting for 7 days but encrypt the logs with an asymmetric encryption scheme like RSA2048.