We present an alternative to the controversial "key escrow" techniques for enabling law-enforcement and national security access to encrypted communications. Our proposal allows such access with probability p for each message, for a parameter p between 0 and 1 to be chosen (say, by Congress) to provide an appropriate balance between concerns for individual privacy, on the one hand, and the need for such access by law-enforcement and national security, on the other. For example, with p=0.4, a law-enforcement agency conducting an authorized wiretap which records 100 encrypted conversations would expect to be able to decrypt (approximately) 40 of these conversations; the agency would not be able to decrypt the remaining 60 conversations at all.

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