Assume each of two parties has something, deliverable electronically, the other wants. Then, a fair electronic exchange is a protocol guaranteeing that either both parties get what they want, or none of them does. (E.g., in certified e-mail, the Recipient should get the Sender's mail if and only if the Sender gets the Recipient's receipt.) Protocols relying on traditional trusted parties easily guarantee such exchanges, but are inefficient (because a trusted party must be part of every execution) and expensive (because trusted parties want to be paid for each execution). Merging Theory and Practice we show how to implement trusted parties in an INVISIBLE WAY, so as to provide fair exchange protocols that are more efficient and much more economical than traditional ones.