Let us stipulate that the wide-faced, twinkly-eyed Irish actor Brendan Gleeson is an under-appreciated thespian who improves every movie he appears in, whether you know his name or not. (Fine, he played Mad-Eye Moody in the Harry Potters.) It is no small thing, then, to say that his compassionate and multi-faceted performance in the gut-punching “Calvary” is particularly good, even for him. Onscreen almost every minute of the film, he bears its weight as skillfully as his character, an Irish village priest, carries the troubles of his parishioners.

The title refers to the hill where Jesus was crucified, and the film begins with St. Augustine’s couplet about the men crucified next to him: “Do not despair; one of the thieves was saved. Do not presume; one of the thieves was damned.” Gleeson’s priest, Father James, maintains this meek, practical attitude as he tends to the needs of his flock. He encourages the weak, admonishes the prideful, absolves the repentant, and does his best not cast judgment beyond the requirements of his job. “I think there’s too much talk about sins, to be honest,” he says. “Not enough about virtues.”

Father James’ steadiness is tested in the very first scene. A man enters the confessional, tells of having been repeatedly raped by a priest when he was a boy, and concludes with the declaration that since the offender is long dead, he will kill Father James in his place, one week from now. (The ticking clock is a far-fetched gimmick, but hey, just go with it.) McDonagh shoots this scene in a single take, the camera focused on Gleeson (we never see the confessor), capturing his wide range of emotions: grief for the man’s suffering, anger at the monstrous priest who abused him, disappointment in his beloved Catholic Church for letting this become an epidemic. This scene alone could serve as Gleeson’s audition reel.

The priest knows who threatened him — it’s a small town; he knows everyone — but he doesn’t want to turn him in, his sympathy for the man outweighing any concern he may have for his own safety. Instead, he goes through the week performing his usual labors, which McDonagh portrays with wicked dark humor. Town vixen Veronica (Orla O’Rourke) has a black eye that she got from either her husband, Jack (Chris O’Dowd), or her African lover, Simon (Isaach de Bankolé). Rich jerk Michael Fitzgerald (Dylan Moran) wants to donate money to the church as a means of soothing his conscience. Gerald Ryan (M. Emmet Walsh), an elderly novelist, asks Father James to get him a gun so he can end his waning life on his own terms. James’ daughter, Fiona (Kelly Reilly) — he was married before he joined the priesthood — comes to visit after a botched suicide attempt.

So, yeah, lots of laughs here. No, really, there are! “Calvary” is less overtly funny than writer-director John Michael McDonagh’s first film, “The Guard” (which also starred Gleeson), but he continues to show an interest in the uncomfortable line between comedy and tragedy. A natural-born wordsmith with the heart of a playwright, McDonagh produces dialogue that’s more than just functional, it’s literary, as when Father James refers to a wine-stealing altar boy’s “Machiavellian chicanery.” The film has much more talking than acting, so McDonagh is wise to give it all the zest he can muster.

In addition to that line between comedy and tragedy, McDonagh explores the ones between life and death and between guilt and absolution. Father James is surrounded by reminders of imminent death: his aging pet dog, the old novelist, his depressed daughter, not to mention his own possible demise. He ponders the concept at the heart of Christianity, the idea that one person can be forgiven through another’s sacrifice. His problem is that there are too many people in his care who need his goodness.

But McDonagh, for all his agility as a writer, stumbles in fleshing out the story. There are inexplicably odd and unneeded characters, such as the male prostitute (Owen Sharpe) who talks like an old-timey Bronx gangster, and subplots that are introduced only so they can serve as red herrings to distract from the main issues. These diversions, while colorful, dilute the power of McDonagh’s central themes. Still, regardless of how the mysteries are solved, it’s edifying to spend time with the imperfect but devoted priest who wants nothing more than to heal people’s wounds.

B (1 hr., 40 min.; R, pervasive harsh profanity, some graphic sexual dialogue, brief graphic violence.)

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