U.S. Solicitor General Elena Kagan, right, argues her first case before the Supreme Court, Citizens United v. Federal Election Commission in Washington, in this Sept. 9, 2009, file artist rendering.

Washington ? Six times in the past nine months, Solicitor General Elena Kagan has come to the mahogany lectern in the hushed reverence of the Supreme Court to argue the government’s case before the justices she now hopes to join soon.

Her arguments have gone like this:

“Well, Mr. Chief Justice, even if you are right, I think that we prevail.”

“We don’t actually think that that’s right, Justice Stevens.”

“I think, Justice Scalia, it’s wrong.”

And so on.

The justices have given Kagan an earful, too.

“I don’t think you really caught what I suggested,” said John Paul Stevens.

“I’m sorry, but that seems rather odd,” said Chief Justice John Roberts.

“I don’t understand what you are saying,” said Antonin Scalia.

And so on.

Oral arguments in the Supreme Court are something of a rarified mosh pit. Meticulously prepared lawyers often struggle to get out a few coherent sentences between the interruptions of justices who tend to be supremely confident that they know better.

An intimidating setting for any lawyer, the venue was all the more daunting for Kagan because her courtroom experience before appearing before the justices was exactly nil.

Yet “General Kagan,” who skipped the government lawyer’s traditional morning suit with long tails in favor of a standard dark suit, held her own and emerged to declare the experience “a great deal of fun.” Kagan is the first woman to serve as solicitor general, the government’s top lawyer at the Supreme Court.

Kagan won one of the two cases that have been decided thus far, but those results have more to do with the strength of the cases she inherited than her persuasive abilities in a courtroom.

“Very few people could do as well as she did with as little experience as she had in that job,” said attorney David Cole, who argued against Kagan on one of her six cases. “One wouldn’t know that she was not a seasoned advocate before the court.”

Kagan, who already knew most of the justices, has parried with them on matters of free speech, terrorism, executive power and more, with a style that was surprisingly conversational for someone so inexperienced.

She mixed in a larger-than-usual dose of humor and showed herself unafraid to disagree with her questioners or to admit she didn’t know something. She also was adept at slipping in well-placed compliments to those doing the grilling, referring to one of Scalia’s past opinions as “brilliant,” and telling Ruth Bader Ginsburg, “You said it better than I did, Justice Ginsburg.”

Court watchers are now scouring Kagan’s courtroom transcripts for clues into how she might interact with fellow justices and handle future cases.

Lincoln Caplan, author of “The Tenth Justice: The Solicitor General and the Rule of Law,” said recent accounts of Kagan’s ability to combine humor, respect and responsiveness to the judges in her oral arguments “suggest that if she becomes a justice she’s likely to be effective in developing working relationships with the other justices, and that’s likely to be useful to her and justices who agree with her on the legal outcome of particular cases.”

Caplan cautioned, though, that oral arguments offer only clues — “nothing definitive.”

Meanwhile, the White House on Saturday asked Bill Clinton’s presidential library to speed the release of more than 160,000 pages of paper, including e-mail, in its possession from Kagan’s tenure as a Clinton adviser in the 1990s.

In a letter to the U.S. archivist, White House counsel Bob Bauer said he was requesting the expedited release to aid the Senate’s review of Kagan’s nomination.