Searching for your next CEO? Don’t be starstruck.

When the hype dies down, a CEO’s legacy will be determined not by fame, but by a different set of factors.

We’re living in the age of “celebrity” CEOs. In this relatively new phenomenon, these executives sign autographs, grace the pages of fashion magazines and even make movie cameos. This month, Elon Musk predicted an apocalyptic end for human civilization, and it went viral. People Magazine captured Sheryl Sandberg’s date with her new boyfriend. Yahoo! Finance even showed Tim Cook shaking hands and taking selfies with Apple customers as he reopened his New York 5th Avenue store.

But while they don’t preclude successful leadership, magazine covers and Instagram followers aren’t the building blocks of effective CEOs. I would argue that the “CEOs of the Future”—the ones who will awe and inspire us—won’t necessarily be the ones trailed by paparazzi. While many executives today have reached celebrity status, thanks to the blurred lines between business, social media and entertainment, when the hype dies down, a CEO’s legacy is going to be determined not by fame, but by a different set of factors.

Having spent decades observing organizational behavior and change management issues, there seem to be certain characteristics of leaders that ultimately lead to solid organizational culture and success.

CEOs of People

The latest CEO Success study found that chief executives are being held to a higher ethical level of accountability than they were in the past. For the first time in the study’s nearly 20-year history, more CEOs were dismissed for ethical lapses (e.g., bribery or sexual indiscretions) than for financial performance or board struggles.

In short, just any public image won’t suffice for tomorrow’s CEO. He or she needs to project an image people respect. And that starts with integrity.

According to a study by PwC’s strategy+business, the CEOs of a hundred years ago, like Henry Ford or John Rockefeller, “were like absolute monarchs.” Pretty much the only way to become a CEO was to build your own company and empire. Often, that meant being ruthless and power-hungry. Fast forward to 50 years ago, and most CEOs were white males, like Ray Kroc and Walt Disney, who were managers instead of monarchs, masters of process and bureaucracy. They were just beginning to think globally, and were always strategizing about how to “maximize investor returns.” But there was still great room for development—more diversity and inclusion and greater incorporation of philanthropy, leadership principles and strong corporate culture.

CEOs of Leaders

PwC defines today’s CEOs as agile leaders: “Gone are the days of the reliable five-year strategic plan.” In our dynamic ever-changing society, this need for agility will continue, but I would argue that tomorrow’s leaders will have to, above all, have heart. They’ll need to treat people well. They’ll need to be men and women of their word, and they’ll need to recognize that they don’t always have the answers, but their employees might. Tomorrow’s CEOs will be leaders of leaders.

More and more, executive roles are going to people who are grounded, come from humble and diverse backgrounds and aren’t hiding in corner offices—or behind the flashbulbs of paparazzi. These kinds of leaders are people who lead with participative management, who remain approachable and build teams of teams. Employees of any level can feel comfortable coming to these leaders with problems or suggestions.

This is how you earn loyalty—and fostering loyalty is going to be very important in retaining tomorrow’s employees, for whom job-hopping will be a common practice. Already, 75% of employees under 34 think job-hopping is beneficial to their careers. Loyalty engenders trust.

I recall hearing about a late-night encounter between James Schenck, PenFed’s CEO, and one of our janitors after most of the employees had gone home for the night. James queried the janitor about his background and future plans. Impressed by his desire to have a better life, James ended up mentoring this gentleman, and ultimately helped him get a higher-paying job where he could use his head instead of his hands. This lack of arrogance, this level of genuineness, astounded me. Can you imagine the transformation of corporate culture if all CEOs were as committed to the success of employees at even the lowest pay level in their organizations? Leadership from the front inspires others to imitate these caring qualities.

CEOs of Business

Tomorrow’s CEOs won’t always be obsessing about their bottom line. They will do what’s right because, well, it’s just right. Consumers respect that. It’s why 88% of consumers want to shop with brands that help them make a difference in the world. And it’s why 86% of workers between the ages of 22 and 37 would consider taking a pay cut to work at a company with a strong mission and values.

The CEOs of tomorrow are also going to have to be increasingly creative. They’ll have to think outside the box, share their wisdom, find solutions to unexpected problems, and hire employees with imagination. That’s because the problems of tomorrow are probably things we’ve never heard of, and the technology that will solve them probably hasn’t been invented yet.

Twenty years from now, it’s not just technology that will be different. Corporate culture will look nothing like it did 20 years ago. The 9-to-5 workday is already becoming a thing of the past as flexibility and remote roles become more popular. Alternative education, like apprenticeships, will be replacing traditional education models as education costs rise. Work-life balance will become increasingly important, as more companies implement mindfulness programs, build meditation rooms and offer in-house childcare. The CEOs of the future are going to have to embrace not just innovation but adaptability. For example, they will have to be the head recruiter and socialize their vision and values at universities, colleges or trade schools to inspire and attract employees to their organizations.

Public image is undoubtedly important when it comes to executive leaders. A famous CEO can also be a great one—look at JPMorgan Chase’s Jamie Dimon, Bank of America’s Brian Moynihan or Amazon’s Jeff Bezos. External relations—building coalitions, networking and engaging with the media—is part of the job. CEOs should be outfacing, well-spoken representatives of their organizational brands, and sometimes this means becoming their own offshoot brand.

But a great CEO’s integrity and honor should always carry far more weight than fame. As boards of public and private companies across the country look to hire their next executive leaders, they should consider that a “celebrity” within a company—someone employees admire and relate to—might look a lot different than a celebrity in the public eye.