(FORTUNE Magazine) – The New York Stock Exchange now wants boards of directors to meet without their CEOs. What should they be doing in there?

Ken Langone, chairman and CEO of Invemed Associates, lead director of Home Depot, and director of General Electric: "At Home Depot we do it over lunch. To get maximum value, nobody can be identified as having made specific remarks. I typically ask, 'What's on your mind? Anybody got any problems or concerns?' You try to make sure that everybody weighs in, so as lead director I provoke people: 'What do you think about that, Paul? Harry?' Then, at the full board meeting, I tell Bob [CEO Bob Nardelli], 'We're a bit concerned about this....' If it's personal, I'll go see Bob alone.

Now, at GE, we're starting to meet separately. A lot of old-style CEOs would have trouble with this. Today it takes a different type of CEO."

Jim Kilts, chairman and CEO, Gillette: "It's one of the things I started here. Before every board meeting there is a separate meeting of the outside directors, even if it's only for five minutes. The chairman of the board committee that relates to the particular area of discussion chairs the meeting. Does this undermine the CEO's authority? Not at all. It's healthy. You've got to have the openness and the questioning of the CEO to make sure that all oars at the company are pulling in the same direction."

Ram Charan, advisor to FORTUNE 500 companies and co-author with Larry Bossidy of Execution: The Discipline of Getting Things Done: "When something's wrong with a company, there's usually at least one director who senses it. The problem is, the outside directors don't have a forum where they can discuss it without the CEO. I've always advocated that there should be executive sessions without the CEO, twice a year, for up to a half-hour. The awkwardness of politeness evaporates, and nobody feels awkward raising a question. These are some of the best brains in the world, and some of the best questioners, but the group dynamics of politeness prevents people from using their leadership skills effectively."