Fairness may be a desirable property of a non-repudiation service. Protocols can achieve fairness through the involvement of a trusted third party but the extent of the trusted third party's involvement can vary between protocols. Hence, one of the goals of designing an efficient non-repudiation protocol is to reduce the work load of the trusted third party. In this paper we present a variant of our fair non-repudiation protocol which appeared at the 1996 IEEE Symposium on Security and Privacy, where the trusted third party will be involved only in case that one party cannot obtain the expected non-repudiation evidence from the other party. This variant is efficient in an environment where the two parties are likely to resolve communications problems between themselves.