The "epic late-night war" between the two comedians is explored in PEOPLE's exclusive sneak peek at Sunday's episode of CNN and Cream Productions' six-part docuseries, The Story of Late Night.
"It was a huge deal about, who's gonna get the throne?" comic Billy Crystal recalls in the new clip.
Rob Burnett, who executive-produced the Late Show with David Letterman, adds: "Dave is the obvious choice, he has sat at that desk, he's been a loyal soldier and he's the best guy on TV, what more do you need? It turns out that you do need something else."
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"Jay had the secret deal," says Jimmy Brogan, a monologue writer at The Tonight Show with Jay Leno.
Rick Ludwin, the Vice President of NBC from 1983 to 2012, then explains, "Jay Leno had just signed a new deal that guaranteed Jay The Tonight Show, whenever Johnny [Carson] stepped down."
"It was part of his re-upping as the guest host and that was set," Brogan recalls.
Ludwin then reveals that Letterman's demeanor was a factor in giving Leno the "secret deal."
"Dealing with Dave had become bothersome and draining, and he could be unnecessarily rude to network people — not just me," says Ludwin. "So did that factor into my decision as to going with Jay Leno over Dave Letterman? You bet it did."
Leno, 71, went on to host The Tonight Show from 1992 through 2009. After a brief hiatus during which Conan O'Brien took over, Leno returned to his post in 2010 and remained there until handing the show off to Jimmy Fallon in 2014.
The year after Leno began at The Tonight Show, Letterman, 74, concluded his NBC show, Late Night with David Letterman, and took his hosting duties to CBS, where he helmed the Late Show with David Letterman from 1993 through 2015.
The Story of Late Night airs Sundays (9 p.m. ET) on CNN.