We present an electronic payment system offering a new kind of tracing mechanism. This mechanism is optimistic fair, as any misuse of the tracing mechanism is prevented by using an audit concept so that a violation of privacy can be detected and will be prosecuted. Thus, compared to previously proposed tracing methods our optimistic fair tracing approach offers more privacy for customers and does not need any trusted third parties, which simplifies the infrastructure of the payment system. Our payment system is able to defend against blackmailing, kidnapping, and bank robberies and can also be used to support investigations of money laundering and illegal purchases.