I’ve tried for days to figure out how to headline this item, and nothing quite felt right: “I Saw Mike Bartlett’s Cock”? “Cock Is Tasty”? Then again, the very difficulty of talking openly about sex is one of the main themes of this extraordinary new play, now running healthily at Manhattan’s The Duke on 42nd Street. So maybe British author Bartlett had more on his mind, in titling his 90-minute four-hander, than merely attracting notoriety. (Though notorious it is; the NY Times and other publications won’t even speak of it as anything except “Cockfight Play.”)

Even that euphemistic title is on target, because what we see played out at The Duke is a cockfight in more ways than one. The setup is deceptively simple: John (Cory Michael Smith) is a young impressionable Brit stuck in what appears to be a long, emotionally abusive relationship with an older stockbroker known only as “M” (Jason Butler Harner).

While they’re “on a break,” as are-we-or-aren’t-we breakups tend to be referred to these days, John has sex with “W” (Amanda Quaid), a working gal he casually chats up most mornings.

To his astonishment he likes it, so much so that brand-new visions of marriage, kids and a “normal life” seem tantalizingly close to fulfillment.

Bartlett’s characters, even those not fully named, are precisely detailed and multidimensional. There’s a bit of the bully about both M and W, and clearly John is a young man who is comfortable in a more submissive role. Yet part of him yearns for respect, and each of John’s lovers is capable of great tenderness at the appropriate moment, rendering his inability to make a choice that much more understandable. M, in particular, is able to swing from hauteur to cringing neediness in record time, making him a true wild card at every stage of the proceedings.

Sex is the topic, much talked about. Indeed it’s all talked about, because as mandated by the text the cast performs the entire play without props or scenery. They’ll talk about handing each objects or sitting down to dinner, but all we see are four actors moving around a circle, never doffing so much as a sweater and barely touching.

The effect of this is to focus our attention away from the sexual dynamics and onto the way intimacy is spoken of. By setting nudity and explicit business off the table, the play points like a laser at the verbal nature of sexual politics: the way a request to one’s lover, for instance, can become a veiled threat and then a naked one. Much of the play’s riotous humor stems from wordplay, as when John’s casual comment to M that W is “rather manly, actually” becomes a trope picked up on, and juggled by, each of the characters over time. (And yet it’s not just a gag because we understand John’s motives; in a crazy way he seems to think calling her “manly” will lessen M’s pain at the thought of the lad’s moving to the other team.)

I hope I’ve given enough sense of the stakes involved to suggest that when these three are thrown together (at a dinner party broker M has brokered to force John to a choice), blood will be spilled and feathers will fly as if this were taking place in a barrio basement.

Love triangles are a familiar dramatic staple, and this one isn’t even 100% original. Actually, the premise pretty much follows the plot of the 1971 movie “Sunday Bloody Sunday” rather closely.

But “Cock” is neither predictable nor familiar. By virtue of the care with which Bartlett has set up his characters, we’re consistently thrown off guard by them and wondering what they’ll do next. A fourth character, M’s Da (Cotter Smith), a working class bloke who loves his son and wants him to be happy with John, intrudes on the party.

He leavens the tension with additional humor, even as his heterosexuality gives W some pungent talking points when she susses out what’s really on his mind.

The Duke is set up as a literal cockpit: Miriam Buether’s circular arena of five rows of naked plywood looking down on the cast, with a stage manager on the floor off to the side cueing scene changes. You have to believe me, some of the best stage pictures of the year are to be seen as helmer James Macdonald deftly moves his cast around like one of those toy theaters in which magnetized cardboard figures are manipulated from below. The angles at which the characters are placed to each other, and the changes in their relative proximity, speak volumes about what’s going on under the surface of the brittle, witty party dialogue.

The cast is sensational. I was worried that the choice to keep the characters English would require me to forgive, wincingly, the accent work. But even if it’s not perfect, some of the resonances of class and education would be lost if the play were Americanized.

“Cock” vaults toward the top of that very short list of contemporary plays whose finger is squarely on the pulse of how men and women, of whatever orientation, sexually interact. It’s probably not as good as “Betrayal” though significantly better than “Closer,” and anyone taken by either of those plays will not want to miss it.

Thin, tiny pillows are provided, offering very little protection for one’s backside. But the discomfort of the hiney isn’t nearly as provoking as the discomfort of the heart as this wild, sad cockfight plays itself out.

“Cock” is running indefinitely at The Duke on 42nd St. in Manhattan, Tues – Fri at 8, Sat at 2:30 and 8, Sun at 3 and 7. Some Student Rush may be available. Ask for Row E if you need back support. www.cockfightplay.com.