(FORTUNE Magazine) – Ann Fudge is a Harvard Business School alum, General Electric board member, wife, mother, grandmother, globetrotter, public service advocate, former star executive at Kraft Foods, and--following a two-year sabbatical during which some surmised that she had killed her career--chairman and CEO of ad conglomerate Young & Rubicam. Inside her makeshift office, currently under renovation, on the 12th floor of Y&R's Madison Avenue headquarters, Fudge announces a mission: "We need to redefine power!" She's not so naive as to believe that her new clout as an imagemaker equips her to recast such a mystifying thing as power. But there's no harm in trying. Fudge wants to ditch the conventional definition of the term. "Do we have to follow the boys' scorecard?" she asks.

No, we don't, say more and more women--and that's just the point. Like Fudge, they say they view power differently from the way that men do: They see it in terms of influence, not rank. And many fast-track women are surprisingly ambivalent about what's next. Dozens of powerful women we interviewed tell us that they don't want to be Carly Fiorina, the CEO of Hewlett-Packard (and No. 1 on our Most Powerful Women list for the sixth straight year); many don't want to run a huge company. But there's a fundamental disconnect here. Those very same women also tell us that they foresee the day in which there is parity in terms of gender representation at the top of corporate America. It is a goal that they honestly, fervently want to reach. Which makes us wonder: If these educated, accomplished, powerful women don't seek the biggest jobs, who is going to? To take it one step further: Do women lack power in business because they just don't want it enough?

This is tricky stuff. To some, that question smacks of blaming the victim. But ever since 1999, when FORTUNE began convening its annual Most Powerful Women Summit--a conference that has included the likes of Fiorina, Avon CEO Andrea Jung, Xerox CEO Anne Mulcahy, eBay CEO Meg Whitman, and Oprah Winfrey--it is a question that participants have raised among themselves, in small groups and large, again and again. And as we delved deeper into the attitudes of America's most powerful women--not only in the corporate arena but in government and academia as well--we kept hearing the same rap about power: It's a turnoff. "I'm afraid of it," confesses Fox Entertainment president Gail Berman, who is, at No. 25, the highest-ranking newcomer on this year's list. (To see the list, open the foldout that follows this story.) "Power is in your face and aggressive. I'm not like that," says another newcomer, Jenny Ming, president of Old Navy (No. 42). Power, says Meg Whitman (No. 2), "has a negative connotation." Even Hillary Clinton would rather not embrace the label. "I never think about [power]," Clinton insists. "I certainly understand it. But I don't think about it in relation to myself."

You can dismiss all this as partly about semantics. Substitute "leadership" for "power" and these women most likely wouldn't bat an eye. And yet other data suggest there's more going on than just disdain for a macho word.

General Electric just completed a study of its 135,000 professional workers and found that women quit at a higher rate: Annual voluntary turnover of the women is 8%, vs. 6.5% for the men. (That may not sound like much, but it adds up to 2,025 more women than men a year.) Research firm Catalyst reports that 26% of professional women who are not yet in the most senior posts say they don't want those jobs. And of the 108 women who have appeared on the FORTUNE 50 over the past five years, at least 20 have left their prestigious positions--most of their own volition, like former Pepsi-Cola North America CEO Brenda Barnes (who moved home to Illinois to focus on her family) and former Fidelity Personal Investments president Gail McGovern (now a marketing professor at Harvard Business School). Apparently it's not that women can't get high-level jobs. Rather, they're choosing not to.

Which makes the responses to our Carly Fiorina question less surprising. Most of the powerful women we asked said that they admire her, but they wouldn't want to trade places with her (and practically all of those insisted on anonymity). Fiorina has never relished her role as corporate America's female icon; she would rather be a model for both men and women, she says. Still, the feedback from these women leaders distresses her. "Perhaps they can't relate to the passion and drive I have for the business," she says. In fact, most women say that Fiorina has a drive and tenacity that they simply cannot match--and wouldn't want to.

Indeed, a common strand among those who take on ever bigger jobs is the notion that power seeks them rather than the reverse. "I never sat down and thought, 'I'll major in political science and Soviet studies, get a Ph.D., become a professor, serve in the first Bush administration, become provost at Stanford, and then become National Security Advisor,'" says Condoleezza Rice. "Not planning has permitted me to accept the twists and turns."

These women don't always greet promotions eagerly. When Marge Magner's boss at Citigroup, Bob Willumstad (Citi's new president), told her last July that he was promoting her to CEO of the company's jewel, its $37 billion Global Consumer Group, she replied, "Are you sure?" The promotion (which lifts her from No. 22 to No. 5 on our list) is "a double-edged sword," Magner says. "Yes, I really wanted it, but I have a bit of awe about the role, the responsibility. I'm on the front line. I have people knowing who I am--all this stuff I've avoided until now."

Andrea Jung (No. 3) says that she has never asked for a promotion. Nor has Genentech COO Myrtle Potter (No. 29). Indeed, early in her career Potter rejected two bigger jobs outright. She figured that lateral moves would better develop her talents. "Everyone thought I was crazy--well, not crazy, but naive," says Potter. "Today I tell young people that they need to develop themselves broadly." (She's probably right: Lack of line management experience is the No. 1 barrier to women's reaching the top, according to Catalyst.) During her 12 years at Wal-Mart, Linda Dillman (No. 28) has never asked for a promotion either. "Promotions have come to me before I felt I was ready," she says. Last year, when Wal-Mart CFO Tom Schoewe and then-CIO Kevin Turner told Dillman that they planned to elevate her to Turner's job, she replied, "Tell me what you're going to do if I don't take the job." She recalls, "Their jaws hit the table. They walked me through why I had to take the job. They said, 'We really didn't have a contingency plan.'"

When it comes to professional modesty, "women overdo it," says Citigroup's Magner, herself a model of self-effacement. When she interviews candidates for stretch assignments, she says, women often tell her they're not ready. Men almost never do. Says Magner: "One of the things I tell women is, 'Listen, next time someone offers you a job, don't tell them why you're not capable. Keep it to yourself!'"

While a reluctance to toot their own horn may hinder some women from rising as quickly as men, paradoxically it may also be one of their biggest sources of strength. Jim Collins, author of the leadership bible Good to Great, observes that many women on the FORTUNE 50 share traits with the outstanding leaders he's written about, such as Kimberly-Clark's Darwin Smith and Fannie Mae's David Maxwell. (He has written only about men, by the way.) "Any number of the greatest leaders, when offered the CEO position, responded, 'I'm not qualified' or something like that," Collins says. "It's not that they lacked ambition or were weak. They were willful, but they were always questioning themselves. They were their own hardest graders."

Of course, some women reject the offer of greater power at work because they're not willing to make personal sacrifices. Jamie Gorelick, formerly vice chairman of Fannie Mae, recalls that a few years ago CEO Frank Raines invited her to be considered for the COO job. She declined. "I just don't want that pace in my life," says Gorelick, who has a 15-year-old son and a 10-year-old daughter. Seeking flexibility and more variety in her work, she quit Fannie Mae this year and joined law firm Wilmer Cutler & Pickering. "The dirty little secret," Gorelick adds, "is that women demand a lot more satisfaction in their lives than men do." Asks Hillary Clinton: "Are women willing to pay the price for corporate life? They have to play by the same rules as men do. And right now there are really brutal rules for women who want to have families."

To get to the highest levels of power, of course, something's gotta give. And that something is often children. (In a recent interview, FORTUNE asked U.S. Secretary of Labor Elaine Chao whether she could handle that job if she had kids. After a long pause, she answered, "It would be awfully difficult.") Or what gives is the spouse's job. As we reported last year, more than one-third of the women on the FORTUNE 50 have stay-at-home husbands--as do several of this year's newcomers, such as Gail Berman, Pepsi-Cola North American president Dawn Hudson (No. 50), and Ursula Burns (No. 44), who is Anne Mulcahy's right hand at Xerox. Mulcahy (No. 4) has a stay-at-home spouse too.

If they do have children, women often don't take the most demanding positions until the youngsters are older. That's especially true for single parents. "While my children were growing up," says Shirley Tilghman, the president of Princeton and a renowned molecular biologist who divorced when her son and daughter were toddlers, "I turned down all administrative jobs. So I've never been a dean. I've never been a provost." (Two years ago, Tilghman "was stunned" when the chairman of the committee searching for a new president asked her to become a candidate for the job; she says she didn't know if she wanted it or was qualified for it.)

There's no doubt that unbridled ambition is less acceptable in women than in men. One reason may be that we've seen some women who push too hard, like former Lucent CFO Debby Hopkins, get slammed (see box). But our interviews show that lots of women push for promotion less strongly than men not because they're reining in their ambition but because they really don't hang their egos on the next rung of the corporate ladder. Instead, powerful women often dream of moving on to more meaningful things. Meg Whitman has been saying for years that she will do something in education or philanthropy after her eBay job. Ann Fudge quit her Kraft Foods job "to do something different." During her two years away she traveled with her consultant husband to Thailand and Bali and Morocco, and spearheaded a tutoring program for African-American kids in conjunction with Harvard Business School. "Women are consciously extending power to broader venues," Fudge says. "We used to say, 'We have to make an impact in business.' But now there's a little bit of, 'I tried the corporate life. I liked it. I realized my power'"--and women can now do other things.

Of three major fields--government, business, and academia--women have made the most progress in the latter. Twenty-one percent of college presidents are female, for example, though statistics show that the gains are slowing. And Tilghman notes a drop-off in the percentage of female Ph.D. candidates applying for academic positions. Academia is "becoming more competitive. People are working harder than ever," says Tilghman. "Many women decide that there are too many compromises they have to make."

In government the numbers aren't as good. Women account for 14% of the U.S. Senate, for example, and 14% of the House of Representatives. (Women's reluctance to promote themselves is a main factor: Women are far less likely than men to "self-identify"--that is, decide to run for office on their own rather than at the invitation of their party.) But, says Nancy Pelosi, the House Democratic leader, "I think we'll achieve parity in Congress before we see it in corporate America. That's because the decisions aren't made by the powers that be [but rather by the voters]. It's open season, and women have more control over the outcome."

And what are the prospects in corporate America? Will women ever hold half of the top-level jobs (EVP and above) in major companies, vs. 8% today? Will 250 female CEOs populate the FORTUNE 500, vs. eight now? Yes, declares Fiorina: "I'm willing to put money down!" Yes, says eBay's Whitman--"in 50 years, when I'm 97." Yes, says Shelly Lazarus (No. 16), the CEO of Ogilvy & Mather--though, she admits, "I'm on the lunatic fringe of optimism."

Lunatic, indeed. These CEOs' idealism clashes with reality. Achieving parity at the top in the next generation is possible only if that generation wants it. And those future leaders have a decidedly lukewarm attitude toward business. According to a 2002 study of 4,200 teenagers by Simmons College and the Committee of 200, a women's group, only 9% of girls (vs. 15% of boys) anticipate careers in business. Meanwhile, business schools are struggling to attract more female students. Women make up 36% of MBA students, vs. 47% of medical school and 49% of law school students. Judy Rodin, president of the University of Pennsylvania, reports that young women on her campus are saying, "'You women worked too hard. You're too strung out.' It's the single most worrisome thing to me. They might not want to fill the pipeline." Says Judy Olian, the dean of Penn State's Smeal College of Business: "In our lifetime and in our daughters' lifetime, given the numbers, there's no way there can be parity." Unless, she jokes, "men all die in a plague."

For parity to happen, men's own attitudes about power will have to change. And (cheer, all you optimists!) there is some evidence that this is beginning to happen--that men, too, are growing dissatisfied with the price they pay to rise in corporate America and are looking for the same flexibility and balance that women want. Cathy Chamberlain, whose research firm CTC Inc. tracks gender attitudes for corporate and political clients, says that for the first time in her 25 years of studies, a desire "to make a difference"--something women have traditionally valued highly--has become a priority for men. The attitude shifts are most dramatic on campuses. When Brenda Barnes, the former Pepsi exec, taught a course last year at the Kellogg School of Management and asked her students to write a life plan, "They said things like, 'We saw what our parents did, dedicating themselves to their companies only to get laid off.'" The young men and women "don't want to give their lives over to their jobs." HBS professor Gail McGovern goes further, saying that she thinks that these young men and women will start to change the face of business--eventually creating a level playing field that's more attractive to women.

Until that happens, those leaders who have already achieved power might focus on helping other women achieve it too. Some are better at that than others. Pelosi, who says it is "my responsibility and my priority to advance women," has appointed women to three key House committees that used to be all male. Princeton's Tilghman has installed a female provost and dean of the engineering school. Getting more women to step up depends on "consistently sending the message that the university welcomes and embraces people who have families," she says.

The pressure is on corporate America to do the same. After completing that GE study showing higher female turnover, the company's leadership development head, Susan Peters, recently talked with CEO Jeff Immelt about speeding up efforts to create a more family-friendly company--better opportunities to work flexible hours, share jobs, and stay in one city without stalling one's career. "These are the types of things we need to do," says Immelt. Smith Barney CEO Sallie Krawcheck (No. 14), the fastest mover on the Most Powerful list, agrees. "If corporate America could somehow figure it out and let women get to the top without requiring them to charge hard their entire careers," she says, "we may get there someday."