The salvage of historic shipwrecks involves a debate between profit-oriented salvagers, who wish to maximize profit, and archeologists, who wish to maximize historical value. We use a principal-agent model to derive the optimal reward scheme for salvagers, including a minimum duty of care in conducting the salvage operation. A review of U.S. and international law suggests that, while there is an emerging recognition of the need to devote greater care to salvaging those wrecks that are located, current doctrines provide inadequate incentives to locate historic wrecks in the first place.