Behind TIME’s Cover with Presidents Bill Clinton and George W. Bush

Mark Seliger is used to taking pictures of U.S. presidents. He’s photographed Barack Obama and Jimmy Carter, both in 2010 for Rolling Stone magazine, and Bill Clinton on several occasions over the past decade. But it’s not every day you get a chance to photograph two presidents in the same room, at the same time, for one magazine cover—a TIME cover, in this instance.

On July 9 in Dallas, when former presidents Clinton and George W. Bush shared the stage at the graduation of the Presidential Leadership Scholars program, a new partnership between their presidential centers, they met with TIME’s editor Nancy Gibbs and deputy managing editor Michael Duffy. A few minutes before, they had posed for Seliger.

“It was uncharted waters for me,” the photographer tells TIME. “Typically, when you’re working in these situations the biggest hurdle is time and hoping that you’re going to get your full amount of time. In this case, we were allowed 10 minutes. And 10 minutes go by very quickly.”

For Seliger, the most important part of such a high-profile shoot comes even before you pick up the camera. “I have to have a pretty specific idea of where I want to go,” he says. “I had an idea of how I wanted to position them, and when we got into Dallas, I was able to get a couple of stools [to use on the shoot].” And with only 10 minutes with both presidents, Seliger needed to take a simple approach to the set-up and lighting. “Then once I get there I can be mindful and respectful of my subjects,” he adds. “I can engage with them, work with them and direct them quickly so that we can make a pretty typical photograph as special as possible.”

Seliger had worked with Clinton in the past and remembered his charm—“He’s always engaging and warm, he remembers you,” he says of the 42nd President of the United States. “He tries to make you as comfortable as you’re trying to make him. That’s part of his charisma.”—but it was the first time that he had photographed Bush.

“For the common person, you would probably feel [Clinton and Bush] weren’t necessarily close to each other, but the [Presidents’ club] is a very small club,” he says. “They are very warm to each other and connected. Bush was equally as warm and charming and down-to-Earth. That was the bonus for me: to walk into a situation where it wasn’t all business, [where] there was pleasant and energetic feeling in the air.”

Mark Seliger is a portrait photographer based in New York City.

Olivier Laurent is the editor of TIME LightBox. Follow him on Twitter and Instagram @olivierclaurent.