Adam Clayton, The Edge, Bono, and Larry Mullen Jr. in From the Sky Down. (COURTESY OF SHOWTIME)

As the 1980s drew to a close, the members of U2 had that special problem of being too successful and too full of themselves. Their steady build toward superstardom came to fruition with “The Joshua Tree,” sending them on a global stadium tour, part of which was chronicled in a tediously important, black-and-white documentary called “Rattle and Hum,” in which their earnest enthusiasm for rootsy blues and rock verged on the embarrassingly pedantic.

Alert to their own press, the band began to hear some earsplitting feedback. A new album was due, and it would come only after a painful gestation at studios in Berlin and Ireland, in which U2 spent a year breaking itself down and remaking its sound and image.

Davis Guggenheim’s intriguing rock­umentary about this, airing Saturday night on Showtime, is called “From the Sky Down,” and it gets the members of U2 (Bono, the Edge, Adam Clayton, Larry Mullen Jr.) to take a frank look back at this phase of artistic crucible.

I realize that the angst of millionaires requires the tiniest-violin soundtrack, but here, with the aid of previously unseen footage from 1990 and ’91, it becomes a revealing and even enlightening meditation on the mystery of why some bands stay together and some don’t. And unlike a lot of recent TV documentaries about rock legends (such as Martin Scorsese’s meandering HBO film on George Harrison, or Cameron Crowe’s mash note to Pearl Jam on PBS), “From the Sky Down” is refreshingly blunt and beautifully assembled. It works because it’s about just one thing: the making (and marketing) of an album.

That album turned out to be “Achtung Baby,” released 20 years ago next month, which was ultimately a critical and financial hit, forever dividing the band’s sound into before-and-after periods.

Guggenheim — whose hit documentaries include the Al Gore global-warming harbinger “An Inconvenient Truth” and “Waiting for ‘Superman,” which explored public school reform — is clearly a fan of U2, but his camera is not fixed in a fanboy’s myopic gaze. Hard questions are asked about ego, youth, disputes, divorces, and the sense of identity that can bind four men together in an act of friendship, art and commerce.

The more revealing memories come from the album’s producers and engineers; the most interesting scene is when we watch U2 in 2011 listen to the earliest “Achtung” demo tapes from 1990 (recorded on DAT cassettes!) and wince at the sound. From these tapes emerges an irresistible guitar riff (what would become the hit single “Mysterious Ways”) and a willingness on the part of Mullen, the drummer, to submit to the possibilities heard in the brutally mechanical electro-beats of German nightclubs.

“From the Sky Down” is packed with enough songs and performance footage to stoke a viewer’s romance with U2, but it never loses sight that it is about a technical process. It’s about how all the little compromises can still add up to a more solid creation.

From the Sky Down

(90 minutes) airs Saturday
at 8 p.m. on Showtime.