Grand jury testimony will not similarly further the client's intentions. Strong reasons, said the justices, support posthumous privilege. It encourages full and frank communication between attorney and counsel. It preserves family secrets, things no one else needs to know. Many privileges protect people, in addition to that between lawyer and client.
Any privilege keeps good, and possibly essential, evidence out of court.
Nevertheless, said the Supreme Court, the risk of loss of evidence probably is not that great. Clients informed that privilege will not protect secrets after death probably won't tell lawyers anything they want kept secret. That would attack the very heart of the attorney-client relationship. President Clinton, of course, is a big shot, but the same principles apply to everyone. When you share the inner secrets of your business with your lawyer, or when you tell your lawyer about confidential family matters, you shouldn't have to worry about your attorney's testimony against you.