The story, certainly, has a stranger-than-fiction aspect, and anyone familiar with this period will likely be fascinated by the bold-face names that basically just pass through. That said, the Apple TV+ show provides a snapshot of a window in time that doesn’t quite come to life.

At its core, “The Big Cigar” resembles the recent Paramount+ series “The Offer,” about the making of “The Godfather,” in capturing the rebel spirit that swept through Hollywood in the early ‘70s, fueled by the anti-war movement.

Here, that mentality is embodied by the colorful Bert Schneider (“The Many Saints of Newark” star Alessandro Nivola), the counterculture producer of “Easy Rider” and “Hearts and Minds” who went on to make headlines with his controversial 1975 Oscar acceptance speech for the latter.

Before that, Schneider was connected to Black Panther leader Newton (André Holland), who had already done time in prison and faced an additional sentence when the police framed him, he maintained, for the murder of a 17-year-old girl. Deciding to seek exile, he warily becomes involved with Schneider, who hatched the plan of faking a movie (“The Big Cigar,” explaining the title) to obscure the details of their elaborate scheme.

In a sign of those times, personalities like Jack Nicholson, Candice Bergen and Richard Pryor cross Schneider’s path, but Newton possesses a different kind of real-world star power that the producer clearly finds intoxicating. As Newton reminds him, they’re playing around with his life, not some game, with Schneider often treating the whole experience like a film shoot with production fires to be put out, much to the chagrin of his producing partner Steve Blauner (P.J. Byrne).

Consisting of six episodes that generally run 40 minutes or less, “The Big Cigar” moves reasonably well, while boasting star credentials behind the camera as well, with Don Cheadle among the producers and directing the first two episodes.

The story, however, bogs down at times as both the producer and revolutionary deal with their respective bureaucracies, while Newton wrestles with paranoia – much of it admittedly legitimate – about the police lurking outside every door and listening at every keyhole.

Adapted from a magazine article, “The Big Cigar” bills itself as being mostly true, granting it the license to engage in some flights of fancy when the story would have likely been better served by either giving in to those satirical impulses or rigidly adhering to the facts.

From that perspective the show peaks early when Newton, as the narrator, expresses skepticism that Hollywood will tell his story right. Landing somewhere in between, “The Big Cigar” justifies those misgivings, presenting a wonderfully rich historical moment in a less than fully engaging way. In terms of reaching the top tier of limited series, score that as close, but no cigar.

“The Big Cigar” premieres May 17 on Apple TV+. (Disclosure: Lowry’s wife works for a division of Apple.)