Martin McDonagh wants to make you wince. He wants to make you uncomfortable and, most significantly, he wants to make you laugh.

The In Bruges Director, less interested in a roundly cohesive plot or internal logic to the little world he’s created in the fictional Ebbing, Missouri than the uncommonly dynamic figures he can deftly create, three of whom are fairly of great note, has here achieved a character study to rival any of his contemporaries that yet, in many other respects, remains greatly wanting.

McDonagh’s latest is a darkly comic and at times dramatic focus on the impact of tragedy on a small town taking place months after Mildred (Frances McDormand) loses her daughter in harrowing circumstances. Lacking closure, she proceeds to furnish her town with the titular billboards to pressure the local police, lead by Chief Willoughby (Woody Harrelson), to find a suspect and bring the killer to justice.

Kicking off with as much a focus on Mildred as on Sam Rockwell’s racist police officer Dixon, an early sequence clearly intended as a macabre jab at political correctness signals that the Director/Writer designs to challenge, confound, instigate and present less than glamorous if unusually complex portraits of what are undeniably unlikeable people. These moments of shock value are less engaging than clearly intended at times not for their being at all gratuitous, with spare moments in the film reaching levels of excessive violence or vitriol, but for their being centered on characters or instances that bear little relevance or consequence to what is effectively a character study of three individuals, the singular if redoubtable achievement of this film.

Mildred confronting a religious leader who objects to the billboards with a cavalcade of invective, however nailing the evident notion of a community sharing collective responsibility and grief for a tragedy, is rendered as a standalone and passing vignette, more akin to an invocation of the themes explored in McDonagh’s previously mentioned Belgian escapade than anything too closely resembling what else transpires in Three Billboards. Likewise, Peter Dinklage’s fleeting appearances, partly consisting of humiliating encounters with locals that are explicitly likened to elements of In Bruges, lack the defined, more fulfilled character arcs afforded only to the film’s three central figures.

Manchester by the Sea breakout Lucas Hedges, here almost completely wasted as Mildred’s son and a grieving brother, is proffered a hint at a storyline signalling his own not inconsequential significance in proceedings as he too rounds on his mother’s actions though is ultimately relegated to a few, largely silent encounters. The presence of Mildred’s ex-husband (John Hawkes) hints at broader issues within the characters’ backgrounds deserving of greater introspection, as does his Charlie and Chief Willoughby both glaringly, and more inexplicably in the case of the former, having partners decades their junior, played by Australians Samara Weaving and Abbie Cornish respectively in two of the film’s further underdeveloped roles.

Harrelson’s Chief is reliably compelling and in fascinating respects a consistent if notably imperfect moral compass, his arc regretfully the briefest of the film’s three mainstays. McDormand has long deserved more prominent roles in major features and here she is the driving, ever-involving force that in spite of Three Billboards’ misgivings will keep viewers transfixed. Together, the two herald the eerily and not infrequently funny moments that pervade the action, though a series of happenstances, coincidences and characters being in the right place (or wrong place) at the right time do little to further the impact of the talents affixed here.

Not the first McDonagh film obsessed with ideas of seemingly insurmountable redemption, Rockwell’s reprehensible Officer, front and centre for a confronting, long-held tracking shot featuring the stalwarts of Ebbing’s ad agency lead by local Red (an underused Caleb Landry Jones), Dixon is too subsequently the subject of a series of sequences that in abruptly disconcerting manners seek to bring into question our perceptions and judgements of this character. This is an achievement in and of itself for a film which trudges ground few others do to deliver something roundly and quirkily unfamiliar.

Nonetheless, however audience members may come to terms with or rest on a consideration of Dixon, together with Mildred their not unrelated arcs, multifaceted and engrossing if culminating in one of the film’s hastily introduced about-turns, bear all the vestiges of this feature’s Daedalian conceits yet nothing so comprehensively and latterly evinced as to greatly surmount long-established notions.

An uneasily disposed assault on senses and sensibilities, McDonagh’s three shrewdly cast complexions are well worth the trip to the cinema and the subsequent debate that will no doubt follow.

Three Billboards Outside Ebbing, Missouri is in cinemas now