Watch David Letterman Share Poignant Foo Fighters 'Miracle' Story

The band also links up with swamp rocker Tony Joe White for a cover of 'Polk Salad Annie' and transforms into a shady law firm

Foo Fighters wrapped up night three of their Late Show With David Letterman residency with another unlikely collaboration and cover song, but the real highlight came after CBS' broadcast ended. In a web exclusive, Letterman joined the band onstage Wednesday night to tell the audience a poignant story about how the Foo Fighters soundtracked a key moment in his fatherhood.

"Years and years and years ago when I became a father, I recognized I was older than most fathers, and so did my son. And so I said I have to find something I can do with my son and we can do it together," Letterman said. He then took his son skiing in the mountains of Montana, and on the last day of the trip, their ski instructor filmed Letterman and his son skiing down the mountain.

The video arrived on a DVD weeks later, and the song the instructor used as a musical bed was Foo Fighters' "Miracle." "This is the second song of theirs that will always have great, great meaning for me for the rest of my life," Letterman said as the band launched into the In Your Honor cut.

On the Late Show, after visits to Nashville and Seattle, the Foo Fighters' Sonic Highways-inspired performances next traveled down south to the New Orleans bayous as the band linked up with pioneering swamp rocker Tony Joe White. Dave Grohl and company joined White for his classic "Polk Salad Annie," a track that was also famously covered by Elvis Presley. Grohl splits lead vocals with White, but it's the 71-year-old rocker who gets to show off the fuzz guitar solo.

One night after introducing "the Foo signal," Letterman had another Foo gag planned: Inspired by cheesy lawyer commercials where longwinded law firm names promise clients easy compensation, the band transformed into "Grohl, Hawkins, Mendel, Shiflett, Smear & Associates." "We'll fight Foo for you," the band says, adding they have 25 years of experience. This might be the first time we've seen Grohl in a suit since this iconic Rolling Stone cover.