But next month, when he's residing over the senate impeachment trial, people will learn quickly that Rehnquist runs a tight ship, CBS News Correspondent Stephanie Lambidakis reports.
"He is a very no nonsense Chief Justice, and I'm sure he will be a no nonsense presiding officer," says attorney Charles Cooper.
Charles Cooper clerked for Rehnquist and has argued before the chief justice many times. His advice for house members who will prosecute the case: don't try any of the antics that marked the house impeachment debate.
"There won't be any theatrical moments while he is presiding." added Cooper.
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One of the things people do know about Rehnquist is that he's a genuine expert on impeachment. He wrote this book on the senate trials of President Andrew Johnson and a Supreme Court Justice. While Clinton's prosecutors in the house are studying his words, Rehnquist in a sense has been ready for this job for years.
"The chief justice will be the person who is most comfortable in his role," says Cooper.
Democrats are still not comfortable with this fact: Rehnquist, a conservative republican appointed by President Nixon, selected the conservative judges that picked Kenneth Starr as independent counsel. But no one doubts that during this high moment in history, the chief justice will make sure that fairness rules.