Tom Cruise had a major request. He wanted IMAX to show his latest “Mission: Impossible” movie — and only his movie — on its giant screens for three weeks. It is the kind of exclusive run that few films get.

So Mr. Cruise went straight to the top. He reached out to IMAX’s chief executive, Rich Gelfond, who had some requests of his own. He wanted all the “Mission: Impossible” premieres, along with press screenings and influencer screenings, to be held at an IMAX theater. And he wanted Mr. Cruise to endorse the company’s screens during his global press tour for the film, which opens this weekend.

“As a joke I said, ‘Tom, no matter what question the press asks you, you’ve got to answer IMAX.’ ‘What’s your favorite scene?’ ‘IMAX,’” Mr. Gelfond, 69, said in an interview. “He agreed to do that.”

In order to get something from IMAX these days, even Hollywood’s top power players have to give some, too.

As movie theater audiences wane and at-home streaming audiences grow, IMAX increasingly stands out as a bright spot in the theater business. The company, founded in Toronto, aims to give moviegoers a more immersive experience with larger screens, better sound and steeper seating, which brings viewers closer to the screen. It now has 416 locations in North America and 1,322 overseas. That is only 1 percent of all the screens in the world, but they often account for a larger percentage of a movie’s box office return, drawing significant crowds for a more expensive ticket than a typical theater seat.

In the past two months, IMAX screens delivered $39 million to the global box office for “Sinners” (out of $321 million total), $30.6 million for “A Minecraft Movie” ($930.1 million total) and $30.5 million for “Thunderbolts*” ($330 million total). (“Thunderbolts*” and “Minecraft” each played in IMAX theaters for two weeks. “Sinners” was brought back to nine locations for a third week.)