Buzz has been building for Jamey Johnson‘s new album, which is set for release this week (Tuesday, Oct. 16). Titled Living for a Song: A Tribute to Hank Cochran, the album does exactly what it says–pays tribute to the late Hank Cochran, one of the greatest country songwriters to grace Nashville in more than a half century.

The album features a huge roster of special guests, including Willie NelsonAlison Krauss, Merle Haggard, Vince Gill, Elvis Costello, George Strait, and Emmylou Harris.

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And last Friday, Johnson and Krauss were the musical guests on The Late Show With David Letterman, where they performed a powerful, show-stopping version of their duet from the album, “Make the World Go Away.”

One of Cochran’s biggest and best-known songs, “Make the World Go Away” was first recorded by country legend Ray Price in 1963. It then became an even bigger hit when another legend, country crooner Eddy Arnold, recorded his version in 1965. The song has been recorded many more times, too, by the likes of Mickey Gilley and even Donnie & Marie. In 2008, Carrie Underwood and Brad Paisley sang it during the ACM Awards (in a tribute to Eddy Arnold).

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Other hugely popular songs written by Cochran that appear on Living for a Song include two major successes for Patsy Cline, “I Fall to Pieces” and “She’s Got You”; “Don’t Touch Me,” which Hank wrote specifically for Jeannie Seely (and it won her a GRAMMY in 1966); “A-11,” which was Johnny Paycheck‘s first big hit (and which inspired another Paycheck song, “Help Me Hank, I’m Falling,” where he pleads for Cochran to write him another); and “Don’t You Ever Get Tired Of Hurting Me,” a hit for Ray Price in 1965 and, 34 years later, also for Ronnie Milsap.

Living for a Song hits stores on Oct. 16.

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– Kurt Wolff, CBS Local