In the early 2000s, Wynton Marsalis often found himself staring at a telephone, full of dread, as he prepared to call fellow musicians – some of them strangers – to ask if they’d be willing to join his septet in benefit concerts for Jazz at Lincoln Center’s Education Program.

“It was worse than being 13 and asking a girl to dance,” the trumpeter said. “Sometimes, I would stall for weeks just getting up the nerve to do it.”

Thankfully, Marsalis made the calls. Also thankfully, artists spanning a wide gap of musical styles accepted his invitations.

The result of these sometimes-unimaginable collaborations is United We Swing: Best of the Jazz at Lincoln Center Galas, a 16-track, various-artists compilation featuring performances recorded between 2003 and ‘07 and released here for the first time.

The LP is a glorious mashup that finds artists from across American music – from bluesman Ray Charles in one of his last performances to former 10,000 Maniacs frontwoman Natalie Merchant – playing a variety of original and cover songs over a bed of big-band jazz courtesy of Marsalis and his mates.

As is often the case with such hodgepodges, some things work better than others. But only John Legend, who sings a hoaky, bosa nova rendition of “Please Baby Don’t,” and Lenny Kravitz, who turns in a languid and ill-conceived version of “Are You Gonna Go My Way,” fall flat.

More typical – and much more enjoyable – are huge surprises such as Eric Clapton playing acoustic guitar and singing a Dixieland take of “I’m Not Rough;” John Mayer singing eerily like Stevie Ray Vaughan on “I’m Gonna Find Another You;” Jimmy Buffett lamenting a life of booze and leisure on a steel drum-laden “Fool’s Paradise;” and Audra McDonald doing a wordless and ethereal duet with Marsalis’ muted trombone on “Creole Love Call.”

Elsewhere, Bob Dylan makes a jazzy shuffle of “It Takes a Lot to Laugh, It Takes a Train to Cry” (a highlight); Lyle Lovett kills on his own “My Baby Don’t Tolerate” (another highlight); and Susan Tedeschi and Derek Trucks take a tack unlike any of their album mates – with Trucks’ slide guitar dominating the septet behind them – making yet another highlight of Nina Simone’s “I Wish I Knew How it Would Feel to be Free.”

The Blind Boys of Alabama, Willie Nelson, James Taylor and Carrie Smith also contribute tasty morsels to this wide-ranging collection, which proves, as Marsalis says in the liner notes, “When it worked, it was exhilarating.”