Over their 31-year run together as multi-multi-multi-platinum-selling avatars of indie rock, the members of R.E.M. never adhered to the tried and true rock-star playbook. Busting out of the musical ghetto once known as “college radio” and into international superstardom, R.E.M. used the sum of its quirks—the deliberately oblique lyrics, the tasteful deployment of mandolin, songs about hairshirts and Andy Kaufman, postpunk intellectualism, and compelling artsy fartsiness—to carve a singular niche and pave the way for similarly thoughtful, left-of-mainstream acts like Death Cab for Cutie and Arcade Fire.

As Rolling Stone’s Rob Sheffield recently characterized R.E.M.’s sweep and influence, “these guys changed everything, creating an entire rock audience in their own image.”

Until one day this fall, when, after more than three decades as a unit and selling some 85 million albums worldwide, the band decided to “call it a day.” But unlike so many rock-group breakups before, R.E.M. managed to sidestep cliché even while parting company. At least according to bassist Mike Mills and frontman Michael Stipe, who insist that no internal power struggles, substance-abuse problems, ego disruptions, or sagging creative mojo were responsible for the band’s demise.

“It seems amicable because it is,” Mills told The Daily Beast. “We are not creatively out of gas. We are not pissed off at each other. There are no issues. The whole point of it is, we’re walking away on a creative high and on our own terms.”

“Save the drama for your momma,” Stipe emphatically added. “If anything, in disbanding R.E.M. managed to do something that’s never been done before in the history of pop music. We did so as friends, with no external forces causing that to happen and without lawyers having to square off. It was just that the time had come.”

The band faced a low ebb in 2004, with the release of its 13th studio album, Around the Sun, which was given the stink eye by critics, sold a lackluster 240,000 copies in the U.S., and compelled guitarist-mandolinist Peter Buck to admit to The Telegraph: “I gave up on the record before we finished it. I knew it wasn’t a good record.”

But that album was not what doomed the group. In 2008, R.E.M. roared back to life with the well-received Accelerate. And on tour for that LP, Buck, Mills, and Stipe began to ponder their future. “We were coming out of a perceived low period into an upswing, and it felt really good,” Stipe recalled. “We did a tour and it felt great. That’s when we started talking about the option to not continue recording or performing.”

As Mills explains it, the idea was to go out while still on top rather than when things were no longer clicking. “We all separately came to the conclusion that this is the time to walk away,” he said. “It has to end sometime. And what better way than on our own terms, when we’re still making great music? We can shake hands and go off on good terms to the next phase of our lives.”

Unbeknownst to fans or even many of their own confidants, Buck, Stipe, and Mills entered the studio last year to record Collapse Into Now, released in March, aware that the end of R.E.M. was nigh. That provided an organizing principle for the album, their best reviewed since the 1990s, when Out of Time (1991) sold 12 million copies and Automatic for the People (1992) sold another 10 million.

“The first song I wrote [on the latest album] was ‘All the Best,’” Stipe said. “If you look at the lyrics, it’s basically saying, ‘We had our moment, it was great. Thanks, everyone. And we hope someone else will pick up the mantle and run with it.’”

Although the bandmates were certainly aware they could take a hiatus, Stipe, Buck, and Mills agreed that severing all professional ties was the right thing to do.

“Of course it was discussed,” Mills said of the hiatus scenario. “But the problem with that is, any work we do subsequent would be overshadowed by ‘When is R.E.M. getting back together?’ We tried to make perfectly clear to everyone that when we’re done, we’re done. Don’t hold your breath for the reunion tour.”

Looking back on their legacy, the musicians can sound alternately proud, defiant, and embarrassed. (Buck was on tour with the singer-songwriter John Wesley Harding and unavailable for comment; original drummer Bill Berry left R.E.M. in 1997.) Mills thrills at the memory of seeing Israeli fans in the desert oasis of Ein Gedi wandering up to a nightclub DJ to request “Oh Life,” their shorthand for R.E.M.’s epochal hit “Losing My Religion.” But the bassist brushes off the lingering perception that the group released its best work decades ago.

“You have to remember, the music that’s always going to matter most to people is the music they’re listening to in high school and college,” he said. “If we had made Accelerate and Reveal in 1982, people would probably love those records and say those were the best.”

Earlier this year, just in time for the release of R.E.M.’s greatest-hits collection, Part Lies, Part Heart, Part Truth, Part Garbage: 1982–2011, Stipe complained of certain “horrendous missteps” in the band’s past but declined to name specifics—a position he maintains. “I purposely don’t like to name songs that I don’t like because it might be your wife’s favorite song of all time,” he said. “And she just doesn’t need to hear it from the 51-year old bald singer of the band that in my opinion it’s a piece of s---.”

“Then there are the things like videos—I took care of all the album graphics and the whole visual aspects of the band,” Stipe continued. “There are tremendous mistakes in there. Bad font choices, T-shirts that I wish did not have our name on it that were sold at concerts, album covers I’m really embarrassed about.”

And in keeping with R.E.M.’s strict cliché avoidance—which didn’t stop Stipe from flashing his penis in a video on his Tumblr account—a farewell tour is out of the question. “Close your eyes and imagine you’re Peter or Mike or me and you’re performing ‘Man on the Moon’ in London, England, for the last time,” Stipe said. “And how would that feel to have 30,000 or 40,000 people watching you and knowing that’s the case? To do that kind of farewell would be mercenary and exploitative. It’s not something we wanted to do to ourselves and our fans.”