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- Congress may impeach the Chief Justice.

- Congress may revoke the power over the FISC, so it isn't irrevocable.

But the FISC Chief is a lifetime appointment, by definition, since the Chief Justice is a lifetime appointment. It is exclusive, because he has executive authority, he does not have to take advice from anyone before making a decision. Whether it is unaccountable is a matter for debate since the operation of the court, and its activities are carried out in secret. It is certainly unaccountable in the normal sense of the word.