Charles Busch really deserves more credit as a master of playwrighting than he typically gets. Mamet steals the limelight for crafty dialogue, Stoppard is the king of intellectual wordplay, but in many ways, Busch has both of them beat. The difference is, Stoppard toys with Shakespeare, and Busch fools around with Debbie Reynolds musicals and Douglas Sirk films. It’s as if he’s being punished for having a gay sensibility.

Who needs acclaim, though, when a production as sassy as The Divine Sister, presented by Uptown Players at the Kalita Humphreys Theater, is doing what good theater should do: Make you laugh and think … although, granted, much of the thinking goes on between fart and dick jokes.

 It’s 1966 in Pittsburgh, and Ste. Veronica’s convent and school has seen better days. Its charismatic Mother Superior (Coy Covington) remains hopefully she can get a prominent Jewish dowager (Mary-Margaret Pyeatt) to allay her guilt by writing a big check. But the millionairess is also an atheist, content with seeing the nuns and their charges turned out onto the street.

Her houseguest, Jeremy (Kevin Moore), feels differently. Twenty years ago, before she took the veil, Mother Superior was a saucy newspaper reporter, trading witty repartee with Jeremy as if they just stepped out of a Howard Hawks comedy. But he dumped her, sending her to the nunnery and rising to abbess. Along the way, she gave up a child and recruited her butch, wisecracking chum (Janette Oswald) to join the order.

All that doesn’t begin to explore the plot, which also includes a postulant (Teri Rogers) with seemingly divine powers, a little gay boy (Pyeatt again) with urges for his bully, a German nun (Lee Jamison) with a mysterious, Cold War motive and the voice of Frau Blucher, an evil monk (Moore) planning something nefarious from the school’s forgotten catacombs and much more. Hey, it’s melodrama — exaggerated complexity is its life-blood.

As complex as the story can be, however, it’s never difficult to follow; and more importantly, it’s almost irrelevant to what makes The Divine Sister such a hoot. It’s the cleverness and the performances that elevate this from mere spoof to savvy comic masterpiece.

Part of Busch’s genius is turning banality into comic potential. Merely praising Pittsburgh as a beautiful city, or off-handedly turning the garbled utterance “can’t face” into the epithet “cunt-face,” a gimmicky use of misunderstand  overused in comedy, but transformed into a ribald riff. (It’s completely spoken between two nuns.) He also drops in countless allusions to other nun-related icons and Old Hollywood classics: When Covington strums a guitar, or lingers just a few beats too long on the word “doubt,” it’s not accidental. He even recreates — and crystallizes — the banter of His Girl Friday into a 30-second tour-de-force for Covington and Moore that’s exhausting to watch. The puns and witty asides and obscure references to old movies go on and on.

Andi Allen, who is as shameless as a music hall comedian when it comes to milking every laugh out of an audience she can, makes sure each moment finds a focus, whether it be using a bible as a sex toy, having Covington longingly stroke a Louisville Slugger while recalling her lover’s enormous member or even having the Mother Superior enter riding a bicycle, but always able to find her key-light.

Allen has an excellent collaborator in Covington, who is the reigning god of cross-dressing theatrical comedy. Covington’s gift is his Eve Arden-like mastery of the ironic pause: He’s always subtly acknowledging that the audience is in on the joke — that he’s a man in a dress delivering hammy lines; he’s his own straight-man. Covington does Busch roles extremely well, but he also adds his own touches, whether it’s a fleeting Cher impersonation or a habit fringed with a slight silver threading to give his garments a dash of glamour.

This is also one of Moore’s best comedic turns. Moore has the square-jawed handsomeness and bland disposition of a ’60s leading man, like Rock Hudson or John Payne or even Tab Hunter — someone as sturdy and appealing as a wingback chair. He’s a marvelous foil for Covington as Jeremy, and a bat-shit crazy monk as Brother Venerius. (Venerius, venereal… get it? Oh, never mind.) As the brusque dykey gym teacher in a habit, Oswald is Kaye Ballard to Covington’s Arden.

Everyone else is just as fine. Jamison gets two over-the-top accents, plus a clingy cat-suit that makes her look like Emma Peel from The Avengers TV series (she’s fast become one of my favorite local comediennes), and Pyeatt plays a pre-teen boy far better than most child actors I’ve ever seen.

Truth be told, there were some defections at intermission on opening night; the gay male couple sitting next to me didn’t crack a chuckle in Act 1, and bailed before the second half. I suppose a lot of people could be offended by the sacrilege visited upon the church (it really does give new meaning to the term “vulgar Latin”). But ultimately, The Divine Sister endorses faith — maybe not institutionalized religion, but the message, just like it was in the old films of the 1950s and ’60s, is one of character and  devotion. Too bad it takes a man in a wimple to get that point across.

The Divine Sister plays through July 29.

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In other theater news, two local shows with gay appeal have been extended. Dallas Theater Center’s Joseph and the Amazing Technicolor Dreamcoat has been extended to Aug. 12, and Theatre Too’s Avenue Q has been extended to Sept. 16 (at least — every performance of the show has sold out the 99-seat theater.)