The first time the phrase “the finest actor of his generation” was attached to Robert Duvall was in a cover story in “American Film” magazine in the fall of 1981.

Duvall already had “The Godfather” movies, “Apocalypse Now” and “The Great Santini” to his credit. But a story headlined “America’s Hardboiled Olivier,” about the actor and his prep and performance opposite the already widely-lauded Robert DeNiro in “True Confessions,” seemed to chisel his reputation, his subtle skills and and range in stone and set the stage for his Best Actor Oscar a couple of years later in “Tender Mercies.”

“True Confessions” is an engrossing but somewhat tentative story of sibling rivalry tucked into an infamous Los Angeles murder mystery.

Duvall plays a detective trying to solve a fictionalized version the infamous “Black Dahlia” murder of an aspiring actress. But the story, based on a then-recent novel by John Gregory Dunne, is really about the corruption of 1940s Los Angeles, as Duvall’s Det. Sgt. Tom Spellacy is a former “bagman,” a collector of illegal cash for assorted crooks, and “once a bagman, always a bagman” he is reminded by those who hold him in contempt.

The corruption isn’t limited to the police, where Spellacy’s partner Det. Frank Crotty (Kenneth McMillan, great at this sort of piggish, unfiltered part) openly takes protection money from local Asian businesses. The plot folds in a Catholic Church twisted by money, in bed with shady characters and in need of cover-ups to maintain its power in the city.

We get a sense of Tom’s distaste for this reputatation in his first visit to his brother, the powerful Monsignor Spellacy (DeNiro), aid and advisor to the Archbishop of Los Angeles (Cyril Cusack). A priest has died in bed with a prostitute. We see Tom’s resentment of his brother, his “you’re no better than me” attitude as he does the power-broker priest this professional “courtesy.”

Monsignor Des Spellacy is carefully maintaining friendly relations with the seedy developer, Jack Amsterdam (Charles Durning) and Amsterdam’s corrupt lawyer (Ed Flanders). Amsterdam’s money put the Church in its present position, brokering Catholic schools into new housing developments, with every parish underwritten and only a lone older priest (Burgess Meredith) complaining about “The Holy Church” being run “like a business.”

Monsignor Spellacy? “I think he’s a better accountant than a chancellor” of the Church.

DeNiro’s Spellacy eats at the best restaurants and golfs with the rich and powerful. He sees the corruption around him, and we gather that he might still have a conscience about this. Or maybe not.

Tom’s resentment fires his investigation of this new, gruesome (“bisected body”) and his efforts to connect “The Virgin Tramp” murder victim, as the press labels her, to the Catholic power structure. He humiliates his brother in public, insulting Amsterdam and their past “bag man” connection to Amsterdam’s face in a tony restaurant. He grinds his teeth over the way their nursing home bound mother fawns over the priest in the family. And he can turn testy, even in the confessional, where he knows he can pin his sibling down and chew him out and Des will have to sit there and take it.

The “uneven” label this film has worn in my eyes and those of others since its release owes to the clumsy way the script connects one circle of corruption to another, to the too-subtle nuances DeNiro brings to his guarded, morally ambiguous priest, and the way that constrasts with Tom’s explosive, woman-slapping temper.

The murder mystery is perfunctorily handled, hardly what you’d expect if you’ve gone to the trouble of folding “The Black Dahlia” (a thigh tattoo) case into your Cain and Abel allegory.

The framing device has the brothers meeting in the early ’60s to make peace, fifteen years after the events in the movie’s fictive present. It sentimentalizes their relationship even as it makes for an apt metaphor for where the power-broker Monsignor ended up — a parish in purgatory (Joshua Tree and environs).

Director Ulu Grosbard, mostly a stage director, doesn’t do justice to the criminal investigation parts of this sordid story. There isn’t much suspense about everything that is coming to a head. But it’s telling that his second most notable directing credit is another story of sibling rivalry, the very fine Jennifer Jason Leigh/Mare Winningham drama “Georgia” (1995).

In a male-dominated movie that leans into the sexism of the times — all-male Catholic organizations, an all white male police department only integrated by Asians in the coroner’s office (the venerable James Hong) — Rose Gregorio — the wife of director Grosbard — makes her mark as a “madam” at “a five dollar cat house” (brothel) who has “history” with Tom, not that he’ll tolerate her getting out of line.

DeNiro, fresh off his Oscar-winning performance in “Raging Bull,” takes pains to lower the heat and play his priest as quiet and thoughtful. That’s a defensible choice, although it does make the sibling rivalry a dramatic mismatch. The Oscar-nominated Meredith shines in his supporting role, as do Durning (a little dance number before the explosion) and the ever-seedy McMillan.

Two TV-stars to be — Dan Hedaya (“Cheers”) and Pat Corley (“Hill Street Blues”) basically audition for the oily roles that would make them famous, one playing a reporter in perpetual need of a shave, the other another corrupt Catholic shaker and mover.

But this is Duvall’s movie, tracking his character as he goes through the jaded motions, finds a reason to take this case “personally” to “settle a score,” and who lives long enough to regret it. He parks this cop midway between “The Great Santini” and his quiet consigliere in “The Godfather,” and he and DeNiro put on a clinic on naturalism in screen acting in their scenes together.

Much is made of any DeNiro pairing with another challenger to the title “Greatest American Screen Actor” that he’s worn for half a century. What makes “True Confessions” a classic is this rare meeting between Mr. Method and “America’s Hardboiled Olivier,” a collaboration of equals, two of the best ever, matching methods and wits in a film that hasn’t improved with age, but which still can be taught in screen acting courses as a grand example of How It’s Done.

Rating: R, graphic violence, nudity, profanity

Cast: Robert DeNiro, Robert Duvall, Charles Durning, Kenneth McMillan, Rose Gregorio, Ed Flanders, Cyril Cusack and Burgess Meredith

Credits: Directed by Ulu Grosbard, scripted by John Gregory Dunne and Joan Didion, based on a novel by Dunne. An MGM/UA release on Roku, Amazon, etc.

Running time: 1:48