Some viewers will be disappointed with John Curran’s film about the 1969 auto accident that cast a shadow over Edward Kennedy’s character—as well as his continued political viability—because they will go to “Chappaquiddick” salivating over the possibility of a right-wing hatchet job on the iconic Democrat, only to be confronted by something more staid and even-handed.

Not that the picture is hagiographical, however; Kennedy certainly doesn’t come off as any sort of hero, and the machinations he and his family’s posse employ to minimize the effect of the tragic death of a young woman on his career are portrayed in an appropriately unseemly light. But the senator comes across as conflicted rather than malign, more puppet than puppeteer. His cousin (and fixer) Joe Gargan, disgusted by the way the matter is being handled, is the far more principled figure.

The screenplay by Taylor Allen and Andrew Logan aims to strike a balance between critique and more empathetic portrayal, laying out in relatively straightforward terms the events of those July days without either sensationalism or apology. Kennedy (Jason Clarke, doing a reasonably good imitation) comes to Martha’s Vinyard to participate in a sailing regatta and joins a party for young women who had worked on his assassinated brother Bobby’s presidential campaign. One of them is Mary Jo Kopechne (Kate Mara), who sympathizes with his downcast mood—he’s brooding over his brother’s death, his loss in the day’s race, and—it appears—the continued disappointment of his father Joe (Bruce Dern), incapacitated by a stroke, in him.

The party is portrayed as a relatively sedate affair. There’s alcohol, of course, but no one seems really drunk, and the interaction of Kennedy and Kopechne is depicted as simply friendly, though a few glances suggest that he might have other ideas. When she says she has to leave for the airport, he offers to drive her, and after he speeds away from a police car to avoid being questioned by the chief about his erratic driving, the car careens off the Chappaquiddick bridge. He escapes from the submerged vehicle; she doesn’t.

It’s his actions afterward that are most controversial. He walks back to the party and enlists Gargan (Ed Helms) and Paul Markham (Jim Gaffigan) to return to the pier with him and try to rescue Kopechne. They fail. He promises to contact the authorities; he doesn’t, for hours. When he calls his father for advice, the old man can cackle out only one word, “Alibi!” He toys with the idea of claiming that Kopechne was driving. He enlists the local sheriff in putting out a press release as self-serving as he and his advisors can manage. He breaks down when calling Kopechne’s parents, but still tries to manipulate the story to his own benefit.

What emerges is a portrait of a deeply flawed, insecure man who vacillates from one tactic to another depending on whom he’s talked to most recently. And when he gets back to the family compound, he’s excoriated by his father, whom Dern portrays as slack-jawed but with piercingly disapproving eyes, and then effectively replaced as manager of events by the family’s brood of hardened advisors, including Robert McNamara (Clancy Brown) and Ted Sorenson (Taylor Nichols). The one decision the senator apparently makes on his own—to wear a cosmetic neck brace to Kopechne’s funeral—turns out to be a public relations fiasco.

Despite Kennedy’s assurance to Gargan that he intends to come clean and resign, he again shifts tack and goes with a carefully-worded televised speech asking Massachusetts voters to decide. And the fact that the crisis is happening at the same moment as the triumphant moon landing allows the Kennedy forces to minimize news coverage and the story is overshadowed by other events.

Allen and Logan set all this out diligently, without italicizing or engaging in extravagant speculation, and Curran presents the events in a sober, deliberate fashion that has the feel of a serious television docu-drama. It’s an approach that results in an account that one can respect for its refusal to sensationalize, but that saps the tale of much dramatic energy. If it works at all, it’s as a portrait of a deeply flawed man who ignored his better instincts, instead embracing tactics focused on political survival rather than honesty.

The extent to which it succeeds in that respect is due largely to Clarke, who brings nuance to the characterization of Kennedy Helms brings a generalized intensity to Gargan, but never entirely escapes the shadow of his comedic roots. Gaffigan is better in that respect, and Dern brings a cruel magnetism to the cadaverous Joe Kennedy—with a few brief strokes he truly epitomizes the raw, uncompromising drive for power that too often informs American politics. The supporting cast is generally adequate, but it’s regrettable that Kopechne remains such a wispy figure; Mara can’t give the real victim her due, especially since the film emphasizes that Kopechne survived for some time in the submerged car, and might have lived had help gotten to her faster, which makes Kennedy’s dilatory action all the more horrifying.

“Chappaquiddik” is technically sound, with solid but unremarkable work from cinematographer Maryse Alberti, production designer John Goldsmith and editor Keith Fraase, as well as an undemonstrative score by Garth Stevenson. But the indecisive ending to the actual incident seems reflected in this understated effort to dramatize it.