The charges made against Woody Allen by Dylan Farrow, his daughter, and Mia Farrow, her mother, have resonated throughout American culture for decades. But it took a while for them to really be heard.

That — the story of their finally being metabolized — makes for the narrative arc of “Allen v. Farrow,” a new documentary series on HBO premiering Feb. 21. Dylan Farrow’s 1992 allegation of childhood sexual assault, which she put into writing on journalist Nicholas Kristof’s blog in 2014, was treated as both serious and ancillary to the career of one of the leading American directors of his time. Previously, this accusation had been widely reported (never having resulted in a conviction for Allen) and existed as a free-floating association that alternately stuck or didn’t to Allen’s name. For many, they were part of the penumbra of oddity, along with his having married Mia Farrow’s daughter Soon-Yi Previn, that it was easier not to think about when buying a ticket to “Midnight in Paris.”

This series puts forward an exhaustive telling of Dylan Farrow’s story, accompanied by interviews with her mother, various of her siblings, and family friends. (Allen’s point-of-view is represented, eerily, by an audiobook recording of his 2020 memoir, which consistently does him so few favors as to seem to have been ghostwritten by his worst enemy.) If a punishing watch, it is a valuable thing to have as a part of the cultural record, twice over: It allows, at expansive length, Dylan to meaningfully be heard, and not solely about the worst thing that ever happened to her. And it exists as countervailing force on what had been a cultural tendency towards, if not forgiveness of Allen, then a sort of ambient willingness to forget.

Directors Kirby Dick and Amy Ziering have worked in this sensitive vein several times before, including in last year’s “On the Record,” about allegations against Russell Simmons. Dylan’s story will be familiar to many, but her voice is not; Dick’s and Ziering’s camera provides her space to unfold her story with minimal feeling of coercion or voyeurism. Similarly, Mia Farrow is allowed time to speak, lending gravity and sorrow to the story. That she, multiple times, refers to Allen as “the great regret of my life” feels both like effective emphasis by restatement and proof of this story’s taking the scenic route, insistent on being less explosive than deliberate.

What is new here are not necessarily revelations but indications of degree. The mistrust between Woody Allen and Mia Farrow, for instance, ran so deep as to yield video recordings of Dylan’s accusations against her father shot by Mia, as well as taped phone calls between the two parents. The antipathy within those calls is striking, as is Allen’s cold insistence on his rightness. Similarly, Allen’s reading of his own memoir seems a major journalistic coup rather than just a reairing of publicly available material, so rigid is he in his sense of conspiracy against him. The Connecticut criminal investigation, too, is plumbed in a way that, to many viewers, will suggest that a lack of conviction is hardly the end of the story.

But there can, throughout “Allen v. Farrow,” come a point at which embroidery around the edges of the Farrow testimony takes away from the story being put forward for the record. Early recounting of just how successful Allen’s career was feels simply unnecessary for most viewers, if perhaps important for some future audience. But several cultural critics’ detailed recounting of, say, the variety of romantic partners Allen cast for himself onscreen seems less relevant than an attempt to over-prove a case that already, for many viewers, holds merit. That Mariel Hemingway played his teenaged lover in “Manhattan” is indeed a wince-inducing artistic choice. That most of his onscreen relationships featured a power dynamic slips further from pertinence.

This had been a perennial problem in covering Allen and the allegations against him. He has worn his peccadilloes so proudly that allegations of behavior that is actually criminal and deeply wrong tend to get tied up with observations of traits that are merely weird. (If this is a conscious strategy by Allen, it’s a very effective one.) It’s when the documentary takes a global view of Allen — his oddities as a filmmaker, say, or the defenses various actors have made, with various degrees of passion, on his behalf, which the series implies without outright saying are part of a coordinated PR push — that it loses some of its surefootedness. What seems in the main to be on trial here is Allen’s conduct within the Farrow family. Allen’s strangeness, and his power in Hollywood, have roles to play in that story, but they can cut against it, too. Dylan Farrow’s story is that of a daughter alleging the most primal sort of violation by the man she considered her father. Distractions are just that.

This work is imperfect. One senses in the voices of cultural commentators employed by Dick and Ziering a desire to place a new spin on questions of “separating the art from the artist” and of perceived great men escaping culpability. The series is neither equipped to answer these, nor, at its best, about them. “Allen v. Farrow” is also, by its nature, one-sided: Farrow has been excoriated by both her son Moses and by her daughter Soon-Yi, and while Moses’ critique is responded to within the series, neither party shows up. Farrow is evidently a complicated individual, but it is not she who is facing down charges of sexual assault. A narrowness of focus at key moments, shutting out both the noise of grand questions and of the extraneousness that tended to accompany the Allen-Farrow coupling, helps make Dylan’s story come across most clearly when it counts. When this series works best is in the moments it most resembles another recent project of its type, the Michael Jackson documentary “Leaving Neverland.” That film was tightly focused on testimony rather than expansive evaluation of the Jackson career and legacy; its accusers, like Dylan, had stories they were ready to tell.

One begins watching this series with a sense of concern for Dylan — not that she will be poorly treated by the filmmakers, who evince obvious care for their subject, but that she may be unable to get through it. Indeed, at one point she appears to be in physical pain recounting her story, overcome by the bodily manifestations of panic. By the end, though, her testimony seems to have allowed her to break through and even to talk about other aspects of her life, if sparingly. She strikes the viewer as having, potentially, a future. For Allen — whose directing career in the U.S., once metronomically predictable with a new film released every year, now seems to be over, and whose memoir he reads from a testament of grievances was dropped by a major publisher and went widely ignored — triumphs exist only in the past. Justice of a public sort was meted out before “Allen v. Farrow” came to be. That Dylan gets a chance to speak out represents for her, one might hope, a closing of this chapter and, perhaps, a chance to start anew.

“Allen v. Farrow” debuts Sunday, Feb. 21 at 9:00 p.m. ET/PT on HBO.