NEW YORK (AP) – Elizabeth Edwards set an unusual condition before agreeing to interviews about her new book: She would only talk if the media outlet agreed not to mention the name of her husband John’s former mistress.

The wife of the former presidential candidate and U.S. Senator has appeared with Oprah Winfrey, Larry King and Matt Lauer within the past week to discuss her book, “Resilience,” in which she writes about the affair and her battle with terminal cancer.

The idea of setting ground rules for an interview is hardly unusual in the celebrity world. Sometimes the interviewers, whether with an entertainment or news organization, agree. Sometimes they overlook the restriction. Sometimes it’s a deal-breaker.

Winfrey, who had the first interview with Edwards, agreed not to identify videographer Rielle Hunter, but asked on the air why it was requested.

“Somebody wants to stand in the light that shines on John, that’s one thing,” Edwards said. “If they, somehow, you know, work at destroying my family and my home in order to get in that light, I’m really not interested in them being in the light too much. It’s not about this woman. It’s about this family.”

The Associated Press would not agree to the demand and was twice turned down for interviews with Edwards.

“It’s simple,” said Michael Oreskes, vice president and senior managing editor of the AP. “We don’t let other people edit our wire.”

He said the request was puzzling considering that Hunter’s name was in the news and had been widely distributed. The AP did report Edwards’ quotes from the Winfrey interview about her husband’s 2006 affair in a story, and used Hunter’s name.

On the “Today” show, Matt Lauer said Edwards had asked “out of consideration” that NBC not use Hunter’s name. “We’re a news show,” he said while interviewing Edwards, “but, and out of consideration, I won’t use the name.”

“Thank you,” Edwards replied.

Jim Bell, executive producer of “Today,” said the Edwards interview had been booked without this request being made. If it was done as a demand, “Today” would not have done the interview.

Still, the request had the same effect.

Given the interview’s subject matter – Edwards’ battle with cancer, the loss of a son and her husband’s affair – “it was a courtesy, not a condition,” Bell said.

In a “Larry King Live” interview on CNN Tuesday, Hunter’s name was not mentioned. King talked about the affair at some length, even asking Edwards whether she was curious about “the woman” and wanted to meet her. (“I don’t think that’s a very useful experience,” Edwards replied.)

King said Edwards had requested Hunter not be named “out of consideration,” and CNN agreed.

Edwards’ attorney, Bob Barnett, referred questions about the interview requests to David Drake, publicity director for publisher Broadway Books. Drake did not immediately return telephone and e-mail messages.

The taste for celebrity news, and the competition for it, can sometimes tip the balance in favor of celebrities – or at least make them feel it has. Actress Angelina Jolie recently asked that reporters sign a promise not to ask questions about her family. Reality TV star Kate Gosselin, facing rumors that she and her “Jon & Kate Plus 8” husband were cheating on each other, is trying to publicize a book without having reporters ask about her marriage.

Comic Sacha Baron Cohen once demanded questions be submitted several days before an interview, to help him come up with Borat-like responses. The trend is present in sports, too, when publicists say “baseball questions only” in a clubhouse to avoid embarrassing stories.

Sometimes it can get truly bizarre: Billy Bob Thornton, talking about his rock band with CBC Radio in Canada, grew angry when his interviewer introduced him as an “Oscar-winning screenwriter, actor and director.” Thornton said, “You were instructed not to talk about … that.”

These are difficult questions for news organizations in tough financial times, too: Do you reject a potentially marketable interview for journalistic principles?

Kelly McBride, ethics group leader at the Poynter Institute media think tank, said readers come to news organizations expecting that its journalists are making decisions on their behalf, not at the behest of their interview subjects.

“The name of the woman is relevant to the story and the decision about whether to name the woman or not should be made by the editors and reporters doing the story,” she said.

AP-ES-05-13-09 1710EDT