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We present a new protocol that allows two players to exchange digital signatures over the Internet in a fair way, so that either each player gets the other's signature, or neither player does. The obvious application is where the signatures represent items of value, for example, an electronic check or airline ticket. The protocol can also be adapted to exchange encrypted data. It relies on a trusted third party, but is "optimistic," in that the third party is only needed in cases where one player crashes or attempts to cheat. A key feature of our protocol is that a player can always force a timely and fair termination, without the cooperation of the other player, even in a completely asynchronous network. A specialization of our protocol can be used for contract signing; this specialization is not only more efficient, but also has the important property that the third party can be held accountable for its actions: if it ever cheats, this can be detected and proven.