In terms of the awards season, all eyes will surely be on Frances McDormand in Martin McDonagh’s “Three Billboards Outside Ebbing, Missouri,” which premiered at the Venice Film Festival Monday. But while the actress delivers a more nuanced turn than the fire-breathing character you might expect from the film’s trailer, it’s Sam Rockwell who really punches through the ensemble with a dramatic arc and a reminder that the journeyman actor can be one of the best tools in a director’s arsenal.

Rockwell stars as hateful Missouri law officer Jason Dixon, clearly a few bricks shy of a load, a simpleton who is the product of his limited environment. But he’s by no means a caricature. Jason has deep admiration and love for Woody Harrelson’s noble Sheriff Bill Willoughby, under fire from McDormand’s scorned Mildred Hayes, who seeks justice for her raped and murdered daughter. He lives at home with his rough-around-the-edges mother, whom he cares for and about. But he’s quite vile, notorious for beating suspects (particularly black ones), an alcoholic drowning his small-town woes at the bottom of a bottle.

All of this is of course conveyed with McDonagh’s trademark repartee on the page as his characters bounce off each other with one-liners and ball-busting candor. So the overt dramatic stakes are held in check by the writer-director’s lighter touch. But he has still provided perhaps the greatest opportunity for his actors yet.

As mentioned, McDormand is given more notes to play than mere indignation over a stalled investigation. One moment in particular in an interrogation room with Willoughby adds a whole other shade to a relationship you assume is one-dimensionally antagonistic. She is absolutely a strong contender in the crowded lead actress race. But Rockwell deserves supporting recognition for the emotional journey he’s able to convey with his character. The actor is a “revelation,” Variety critic Owen Gleiberman reported out of Venice, giving “a high-wire performance, daring to make himself gnarly and dislikable, only to undergo a transformation that the actor, mining his moonstruck ability to win laughs in even the most disturbing situations, makes spiritually convincing.”

And there’s obviously a narrative to work with here. Rockwell, who was just cast as George W. Bush in Adam McKay’s upcoming “Backseat,” has delivered in films like “Confessions of a Dangerous Mind,” “Moon,” “Conviction” and “Choke” over the years. He’s also been a vital cog in Screen Actors Guild-nominated ensembles like “The Green Mile” and “Frost/Nixon.” But he’s never really been in the Oscar mix. Perhaps it’s time.

“Three Billboards” is a unique film in Fox Searchlight’s 2017 stable, which also includes Guillermo del Toro’s ornate fairytale “The Shape of Water” as well as Jonathan Dayton and Valerie Faris’ emotional “Battle of the Sexes.” It’s a whole other tonal gear. Though McDonagh does have an Oscar for the 2004 short film “Six Shooter,” the Motion Picture Academy has yet to really respond to his feature work outside of a screenplay nomination for 2008’s “In Bruges.” His latest has even more going for it so multiple Oscar nominations are definitely on the table.

The film goes on to the Toronto Film Festival next week before releasing on Nov. 10.