I had never heard of the so-called “Irish Curse” before writer Martin Casella and director Matt Lenz named their play after the anatomic misfortune of having a small penis. I expected this play about the support group held every Tuesday in a Brooklyn church basement to be a silly, somewhat mocking look at these obsessive men, or maybe a brash parody similar to “Menopause: The Musical.” But “The Irish Curse,” in addition to being funny, is also profound, finding tragedy as well as humor in the all-too-common plight of these poor men.

Despite a premise practically begging for over-the-top treatment, “The Irish Curse” is more naturalistic than the average Fringe play, boasting realistic dialogue, spare blocking, and restrained actors who speak conversationally onstage. Here we have a jolly priest (William McCauley), a good-natured jock (Brian Leahy), a gay cop (Howard Kaye), a genteel Southern gentleman (Eddie Korbich), and the group’s only Irishman actually born in Ireland (Roderick Hill). If a Catholic priest were to host a support group in his church’s basement for men with small penises, it probably would look a lot like this.

This is a subject often joked about superficially, but never really (as far as I know) tackled in depth as it is here. This makes “The Irish Curse” a definitive take on the anxieties and tribulations of the less-than-impressively endowed male. Its characters wonder what they did to deserve this life of inadequacy and failed relationships, scoffing at the claim that size is irrelevant while recognizing that much of their misery is self-imposed. They are maddened by the obliviousness of genes to the social consequences of its spiral ladder: What kind of universe do we live in when the one thing you can’t choose – your DNA – rules so much of your life?

The play’s slogan is “anatomy is destiny.” The old man from Georgia theorizes that wars, Irish drinking, and the prevalence of Irishmen in the priesthood all result from penis insecurity. And when Father Kevin – who gently moderates the discussion for most of the play – finally lets loose about why he joined the priesthood, he admits that at least part of the Southerner’s theory might be true.

Though the play doesn’t jump immediately into the subject at hand, once it does, it has a strict devotion to its one issue and never strays. In a lesser play, especially one as dialogue-driven as this one, this would get old fast. But “The Irish Curse” sustains its relentless concentration for an hour and 45 minutes. The writing and acting are just that good.

Most of the characters aren’t just variations on stereotypes or mouthpieces for various theories. They come to life as people. The exception is the self-hating gay cop, Stephen: The writers have fallen into the literary trap of creating a character fascinated with his own homosexuality and overly curious about who else is gay. The token non-P.C. character, he’s accused of joining the force merely to pack a piece; he also feels guilty for arresting Korean battery sellers and sending poor immigrants back to Colombia. Such a person is possible, but seems more like a playwright’s wishful thinking.

Even when “The Irish Curse” gets highly emotional, it never devolves into melodrama. It doesn’t rely on a twist ending or a neat resolution. The five men acknowledge that their battle is just as futile as Father Kevin’s no-profanity rule. The best they can do is change their attitudes, which might be just as inalterable as their genes. They’re resigned to their destiny, but none too happy about it.

August 19, 21, 24 & 25 (440 Lafayette Street, between Astor Place and E. 4th Street, 212-279-4488).