The most thrillingly experimental five-year period of Mitchell’s career is chronicled comprehensively — across seven hours of music — in the fourth volume of her consistently revelatory Archives series. “The Asylum Years” finds Mitchell gradually turning away from the more traditional rock sounds that so many of her contemporaries were taking to the bank in the mid-1970s, and instead finding a more expansive musical language in the world of contemporary jazz, eventually collaborating with such fellow visionaries as Jaco Pastorius, Wayne Shorter and Herbie Hancock. The previously unheard early demos of material destined for “Hejira” and “Don Juan’s Reckless Daughter” are fascinating, but what’s clear from the wealth of live material here is that Mitchell honed these ever-evolving compositions on the road, and that being constantly, restlessly in motion during this time clearly stoked her creativity. “I’ve got this tune that has been growing,” she excitedly tells an audience during a stop on Bob Dylan’s Rolling Thunder Revue, by way of introducing “Coyote.” “It started off with two verses and a couple of nights later I added another one, and last night I got a fourth one.” What a joy, to get to hitch along on the ride.

LINDSAY ZOLADZ, New York Times

Elvis Costello, ‘King of America & Other Realms” (Ume)

His 1986 album “King of America” was his pilgrimage toward country and rockabilly, filled with admiration for American music and mixed emotions about 1980s America. Abetted by T Bone Burnett, Costello worked with musicians rooted in the South, including members of Elvis Presley’s band. The six-CD boxed set gathers other unreleased Southern collaborations — with Allen Toussaint, Dave Bartholomew, Emmylou Harris, Rhiannon Giddens and Ralph Stanley — and songs informed by the pithiness of classic country. The set’s peak is a twangy, roistering 1987 Royal Albert Hall concert — mixing Costello’s songs and roots-rock oldies — backed by his American band.

JON PARELES, New York Times

Green Day, “American Idiot (20th Anniversary Deluxe Edition)” (Reprise)

Released six weeks before the 2004 election, Green Day’s bombastic blockbuster seventh album, “American Idiot,” remains one of the defining pop cultural mementos of the George W. Bush era — an epic, hook-stuffed and defiantly ambitious rock opera that gestures broadly toward political unrest and eventual salvation. The previously unreleased demos and rereleased bonus tracks show that from the album’s earliest stages, Green Day was thinking big. The demo of what would become the LP’s climactic suite, “Homecoming,” contains some rough, goofy filler lyrics but already has a complicated multipart structure and a 10-minute run time. Material from two pristinely recorded live sets provide a snapshot of the pivotal moment when these sneering California punks transformed into bona fide arena rockers.

LINDSAY ZOLADZ, New York Times

The Police, “Synchronicity (Super Deluxe Edition)” (A&M)

The fifth, final and best studio album by the Police was polished and tautly controlled. The vastly expanded boxed set reveals instead how elastic the songs were, not just while the Police were working them out in the studio but in their afterlives onstage. Tracks from recording sessions show how the Police carved spaces into their arrangements, decluttering them to add breathing room. And two CDs from a concert in 1983 exult in remaking the grooves yet again, juiced with extra adrenaline.

JON PARELES, New York Times

U2, “How to Dismantle an Atomic Bomb” (Interscope)

U2′s 2004 album was one of the band’s peaks: brash and turbulent, supercharged with guitar riffs but also suffused with longing and loss. The deluxe 20th anniversary reissue is expanded with a dynamic concert set and 10 songs from the same sessions: six that would be reworked and eventually released, four previously unheard (and slightly reworked in recent sessions). They’re a glimpse of U2 without its last painstaking layers of studio polish, and all the more immediate for it. The 10 additional songs are also available online.

JON PARELES, New York Times