A documentary by Jeffrey Levy-Hinte. Rated PG. Opens Friday, August 7, at the Cinemark Tinseltown

In 1996, Leon Gast’s When We Were Kings revived the Rumble in the Jungle, that 1974 fight in which Muhammad Ali got up in George Foreman’s grill. Previously, it turns out, there was a spectacular three-day concert in the country then called Zaire, showcasing some of the best American and African musicians of the day.

Art-house filmmaker Jeffrey Levy-Hinte—he produced Laurel Canyon and Mysterious Skin and was an editor on Kings—became obsessed with 125 hours of unused footage shot by four cinematographers (including Albert Maysles). Years of battling for that material have now paid off handsomely in Soul Power, which whittles the stuff down to 93 tight, roughly chronological minutes.

Without adding context, other than occasional title cards, Levy-Hinte shows us the buildup, with workers erecting a stage in Kinshasa, promoters Don King and Stewart Levine holding forth on their project, and musicians flying in from the States.

With flutes, guitars, and some serious shoe-banging, Celia Cruz and the Fania All-Stars easily rule the air. Once they land, Ali is the dominant figure, amusingly speechifying about the pitiful condition of race relations in the U.S. and playfully sparring with Philippé Wynne, killer lead tenor of the fabulously leisure-suited Spinners.

On-stage, there are beautifully shot and recorded visits with B. B. King and the Crusaders, and not quite enough time with Africans, including standout Miriam Makeba. Then comes an explosive finish with headliner James Brown, doing his trademark moves on three numbers. The most surprising highlight is offered by Bill Withers, who mesmerizes the massive crowd with a solo acoustic take of his harrowing “Hope She’ll Be Happier With Him”. The politics, Afros, and butterfly collars may seem dated, but the music remains as fresh as tomorrow.