Paul Shaffer and David Letterman's TV partnership has lasted longer than most celebrity marriages: 36 years and still going strong. Paul speaks highly of his relationship with Dave. "We went on TV every night without rehearsal and just talked, and it was incredible," Paul tells Closer.

"We never really had a disagreement." OK, maybe once: "I said to him, 'Hey, that was rough what you said last night,' and he said, 'Yeah, but you could answer back.'" Paul recalls. "All's fair."

paul shaffer and david letterman getty images

Paul and Dave on the Late Show.

Paul now does the music for Dave's Netflix talk show, My Next Guest Needs No Introduction.

For more on Paul Shaffer and David Letterman, pick up the latest issue of Closer Weekly, on newsstands now — and be sure to sign up for our newsletter for more exclusive news!