Few bands set their sights on such lofty musical or political terrain as British punk trailblazers The Clash. “Death or glory!” its members famously proclaimed, and for all the band’s internal contradictions, that wasn’t just rhetoric.

Its final leaps of faith are on display in The Rise and Fall of The Clash, a flawed but important documentary by Spanish filmmaker Daniel Garcia. The powerful film sets out to explain how The Clash came to eject its most musically adept members, drummer Nicky “Topper” Headon and guitarist and vocalist Mick Jones, at the height of its commercial success. The ensuing “Clash Mark II” period is often omitted from official Clash histories, so Garcia’s attention to that time alone is a needed corrective.

The explanations offered on screen are not always satisfying. For example, Garcia appears to posit that Headon and Jones’ ouster had to do with a “madness” that had infected singer Joe Strummer, bassist Paul Simonon, and manager/Clash co-founder Bernard Rhodes, rather than the musical and political differences exacerbated by the band’s arrival in the Top 10. The corrosive trappings of success drove the band, and Strummer in particular, to revert back to punk-rock basics.

Garcia’s compelling if incomplete telling is unfurled in the second half, following a beginning that feels too much like a Behind the Music retread that rehashes details about Headon’s heroin addiction and Jones’ punk-diva behavior.

If this story was the heart of the film, it might not rate as essential viewing. But when the film delves into the band’s final two years, it takes off with the help of several figures ignored in official Clash histories, like Pete Howard, Nick Sheppard, and Vince White, who joined the band after Headon and Jones were deposed. The new arrivals were in for a far bumpier ride than they expected, facing a steep learning curve and a verging-on-abusive boot-camp regimen imposed by Rhodes. White even bursts into tears on camera, suggesting that while the wounds from those days are now decades old, they’re not yet healed.

No one has told this piece of the Clash story on film, and, as such, it is crucial and gripping. Yet, without Simonon and key associate Kosmo Vinyl weighing in, there’s a hole at the heart of the tale. Often dismissed as a good-looking but vacant “tag-along” of first Jones, then Strummer, Simonon can now be seen as the trio’s most principled and steady member, resolutely opposing a reunion of the band, defending the decision to eject Jones, and affirming the value of the Clash Mark II’s creative output, however poorly served they were by the Rhodes-dominated Cut the Crap album.

In the end, there’s lots of death but not much glory in Strummer and Simonon’s mission to sustain The Clash as both a vital artistic entity and a revolutionary political force. The time was riddled with personal and creative challenges—including the death of Strummer’s parents and struggles with addiction and depression—that interfered with The Clash’s reconstruction. That the drama plays out amidst the Thatcher/Reagan assault that culminated in the breaking of the 1984-85 British miners’ strike and the consolidation of right-wing political and economic power only adds to the pathos.

Diehard Clash fans deserve a more comprehensive history of this time. But simply to hear accounts from long-neglected members, and encounter bits from the “busking tour”—where this multiplatinum band hitchhiked around the economically depressed north of England, singing for free to whomever they encountered—is a profound step toward setting the historical record straight.

Mark Andersen and Ralph Heibutzki’s book about The Clash’s later days, We Are The Clash: The Last Stand of The Only Band That Mattered, is due out late 2013 on Akashic Books.

The film shows at 9:30 p.m. Sept. 23 at Gala Hispanic Theatre, 3333 14th St. NW. $5–$10. (202) 234-7174.