Get your mind out of the gutter.

Yes, the title of Mike Bartlett’s play might seem salacious considering that it concerns a gay couple whose relationship is threatened when one of them falls in love with a woman. But the more pertinent meaning of Cock is as in a cockfight, which this battle of wills among the three parties closely resembles.

The Olivier Award-winning drama currently receiving its New York premiere at the Duke on 42nd Street is staged in-the-round, with the audience sitting on wooden benches surrounding the action and a fluorescent light looming overhead.

One could argue that the presentation is gimmicky, that the play would work just as well in a traditional proscenium setting. But there’s no denying that James MacDonald’s staging adds a greater intensity to the already charged proceedings.

That the piece revolves around the central dilemma of the younger gay man forced to choose between lovers is reinforced by the fact that only he is identified by a proper name, John (Cory Michael Smith).

Competing for John’s affections are his longtime older lover M (Jason Butler Harner) and W (Amanda Quaid), the young woman with whom he has struck up a serious relationship. For a while he lurches back and forth between them until the trio face off at a tension-filled dinner party also attended by M’s supportive father (Cotter Smith), in which he given an ultimatum by both to finally make a choice.

John’s dithering, while certainly exasperating to his two lovers, is depicted in moving fashion. For him, it’s not simply a choice between two people but rather a determination of his sexual identity. For most of his life he has been solidly convinced he’s gay, but his love for W, which is as much physical as emotional, calls everything into question.

Despite their lack of specific names, both M and W are complexly drawn figures. M, a stockbroker who hides his insecurities beneath a barrage of withering quips, is despondent over the possible impending loss of his lover. And W, a divorced elementary school teacher, proves a formidable combatant, as steely and self-assured as she is vulnerable.

And M’s father, a macho type who has reluctantly come to accept his son’s lifestyle, eagerly throws himself into the fray with amusing results.

The dialogue is sharp-edged and funny, and the staging inventive. Particularly effective is a lengthy scene depicting John and W’s first sexual encounter, with the two figures expressing their ecstasy while merely facing each other and engaging in what looks like a two-step dance.

The performers deliver virtuosic performances that further help us identify with each of their characters. When John finally does make his agonized decision, he subsequently collapses into an emotional despair that is shattering to witness.

Despite the clinical nature of its setting, which resembles an operating room theater as much as a fighting ring, Cock proves both deeply moving and uproariously funny. Just be sure to bring along a well-padded seating cushion.

Duke on 42nd Street, 229 W. 42nd St. 646-223-3010. www.Dukeon42.org.