Frances McDormand plays a grieving mother driven by an implacable thirst for justice in Martin McDonagh's darkly comedic drama, also starring Woody Harrelson and Sam Rockwell.

The roadside billboard is an iconic feature of the Americana landscape, with quaintly illustrated graphics welcoming travelers, offering hot coffee, comfort food and a warm hotel bed, or bidding farewell to those departing, often with a folksy "Y'all come back now"-type sentiment. There's no such reassurance in the tattered signage standing abandoned in the morning mist in the opening shots of Martin McDonagh's blisteringly funny and richly textured third feature, Three Billboards Outside Ebbing, Missouri. Instead, they loom like desolate memories of a time of prosperity and happiness, suggesting a Walker Evans image of a Great Depression highway to a place beyond hope.

Accompanied on the soundtrack by the glorious voice of Renee Fleming singing Irish poet Thomas Moore's "The Last Rose of Summer," set to a melancholy traditional Celtic tune, that image catches the eye of Mildred Hayes (Frances McDormand), and from deep within the world of infinite pain and anger she inhabits, a plan takes shape.

After the entertainingly larkish but low-caloric carnage of Seven Psychopaths, McDonagh returns here to the peak form of his debut feature In Bruges, and of his best work for the stage. A stupendous showcase for the formidable gifts of McDormand that also provides plum roles for Woody Harrelson and Sam Rockwell, this is a corrosively humorous drama of festering injustice, Shakespearean rage, grave reckoning and imperfect redemption, which unfolds with the epic dimensions of a classic Western showdown. Fox Searchlight has a real ripper on its hands with this one, even if it likely won't be for mainstream tastes.

It's been months since Mildred heard a word from cops about the investigation of her teenage daughter's horrific rape and murder by incineration, so she takes radical steps to light a flame under the ass of local law enforcement. Following a rudimentary check of the legal restrictions on billboard advertising, she has three signs put up, their blunt messages in boldface uppercase on a blood-red background reading, in order: Raped While Dying; And Still No Arrests; How Come, Chief Willoughby?

The billboards are on a road barely used since the freeway was put in, but police officer Dixon a violent, racist doofus for the ages in Rockwell's wildly undignified performance happens to drive by them on Easter Sunday, while the glue is still wet. "Looks like we got a war on our hands," mutters Willoughby (Harrelson in a role that fits him like a glove) to his horse, after Mildred, dressed for battle in a bandana and coveralls, appears on local TV news to restate her beef with the police.

Willoughby tries to reason with Mildred by sharing his frustration about the absence of leads in the case. When that fails to sway her, he reveals he has late-stage cancer. But Mildred remains immovable, even as the town shows its support for the well-liked, family-man police chief. Her son Robbie (Lucas Hedges), who has tried to bury his grief for his sister, threatens to join the disapproving chorus. And her ex-husband, Charlie (John Hawkes), a wife-beating former cop now living with Penelope (Samara Weaving), a 19-year-old who confuses polo with polio, finds the billboard scheme beneath contempt.

Mildred Hayes is the substantial role McDonagh has written for a woman, and what a role it is. The part was created expressly for McDormand, who brings her to life with a grim fury worthy of Greek tragedy, but also with a needling moral conscience as the rippling consequences of her actions become clear. Tough-talking, staunch and fearless in her almost biblical wrath and refusal to back down, she's a highly original, flawed hero, a no-bullshit, resilient woman who's also quick with a withering comeback when confronted.

McDonagh's peerless gift for zinging, curse-laden dialogue is in full flower here, both in ricochet exchanges and magnificent solo arias, frequently tossing in wicked acknowledgments of casual racism, homophobia and other forms of bigotry that seem fueled rather than quelled by PC awareness. But while the film is corrosively funny, the savage humor never undermines the key characters' well of hurt, whether it's the grief of Mildred, Robbie and skuzzy Charlie, or Willoughby, whose challenges with the Hayes case collide with agonizing decisions concerning his own pain and the extent to which he will allow the family that he loves to endure it.

There are several powerful dramatic scenes here, perhaps none more haunting than a gentle interlude in which Mildred is planting flowers around the billboards when a deer emerges from the woods, prompting tender words and her first display of raw emotion, undiluted by bitterness. Penelope's store-bought wisdom, "Anger begets greater anger," is a point made in semi-mockery, but one that McDonagh allows to sink in with his characters in different ways. And while the film continues almost throughout to generate great whoops of shocking laughter, it's the notes of genuine sorrow, compassion and contrition that resonate.

McDonagh deftly teases the possibility of a cleanly resolved outcome but then pulls back to concede that we live in a divided world in which some atrocities go unpunished and some wounds will never heal, but where a window of forgiveness always remains open. In that sense, Three Billboards nudges close to the moral complexity of Calvary, a criminally underappreciated gem made by the director's brother, John Michael McDonagh.

Shot in North Carolina by British cinematographer Ben Davis in an unfussy style that never draws attention to itself, the film looks sharp, and production designer Inbal Weinberg captures the vintage small-town Main Street charms without overdoing it. More than the visuals, the depth of the movie owes much to Carter Burwell's flavorful, distinctly American score, with its roots and folk elements, and to superb song choices.

The performances could scarcely be better, starting with McDormand, who can add this, alongside Fargo and Olive Kitteridge, among her best work; and continuing with Harrelson, who layers soulful feeling beneath his easy, aw-shucks manner with consummate skill. Rockwell, who has worked with McDonagh both in film and theater, gets one of his best roles with Dixon, whose honest bid to turn his life around still runs up against the limitations of his stupidity. And yet the developments with his character are unexpectedly affecting.

In smaller roles, Manchester by the Sea discovery Hedges makes Robbie a smart young man, very much his mother's son; Zeljko Ivanek (another McDonagh stage vet) brings plenty of bite to a police sergeant; Caleb Landry Jones finds subtle shadings in the local ad-sales agent; an underused Clarke Peters strides in late as a transferring police chief, making it clear with a glance and a few well-chosen words that he suffers no fools; and Peter Dinklage, rocking a mullet and a fat mustache, has poignant moments as a would-be suitor who can't get past Mildred's brittle edges, not for lack of trying. Among the most memorable supporting characters is Dixon's tough old boot of a mother, a hilarious throwback to the vile crone from McDonagh's breakthrough play, The Beauty Queen of Leenane.

Distributor: Fox Searchlight
Production companies: Blueprint Pictures
Cast: Frances McDormand, Woody Harrelson, Sam Rockwell, Abbie Cornish, Lucas Hedges, Zeljko Ivanek, Caleb Landry Jones, Clarke Peters, Samara Weaving, John Hawkes, Peter Dinklage, Sandy Martin, Amanda Warren, Brendan Sexton III, Kerry Condon, Kathryn Newton, Darrell Britt-Gibson
Director-screenwriter: Martin McDonagh
Producers: Graham Broadbent, Peter Czernin, Martin McDonagh
Executive producers: Bergen Swanson, Diarmuid McKeown, Rose Garnett, David Kosse, Daniel Battsek
Director of photography: Ben Davis
Production designer: Inbal Weinberg
Costume designer: Melissa Toth
Music: Carter Burwell
Editor: Jon Gregory
Casting: Sarah Halley Finn
Venue: Venice Film Festival (Competition)
Rated R; 115 minutes