“Dirty Rotten Scoundrels” is a clever and engaging new Broadway musical. That’s the trouble. The show has vexingly good songs, unnervingly elegant sets, and enough strong performances to be really distressing. Composer David Yazbek and librettist Jeffrey Lane have sweetly adapted the 1988 film, which leaves a sour taste. I had a good time, which is bad.

New York hasn’t seen many musicals like this one lately. Broadway has become all but synonymous with post-Lloyd Webber excrescences like “Dracula,” “Brooklyn,” and “Good Vibrations” (a lot of pain to bear in one season, when you tally it up that way). But “Dirty Rotten Scoundrels,” which opened last night at the Imperial, oozes old-fashioned charm. There’s no trace of “American Idol” belting, no interactive gimmicks, no vampires. David Yazbek may throw in a pop reference here and there, but his score maintains a safe distance from the sonic wasteland of Wildhorn. Among his witty touches is a number called “Love Is My Legs,” a satisfying demolition of that bloated style.

The show reunites Mr. Yazbek with his able “Full Monty” collaborators, director Jack O’Brien and choreographer Jerry Mitchell, and puts plenty of talent at his disposal. John Lithgow plays Lawrence Jameson, a tall, preening, smoothly Apollonian con man who stalks his prey on the French Riviera. Early on, his aide-decamp Andre (Gregory Jbara, drily funny and debonair in pinstripes) alerts him to the arrival of an heiress (played by a funny and very game Sara Gettelfinger).

“Married?” asks Jameson.

“Constantly,” Andre replies.

“Money?”

“Her people are in oil.”

“Crude?”

“Well, she is a little pushy.”

Librettist Jeffrey Lane has a knack for this old-fashioned, half-laugh-half-groan shtick. (He comes from television.) The show needs plenty of it once Jameson meets two-bit crook Freddy Benson, played by Norbert Leo Butz as grubbier and more grasping than Jameson. Like his co-star, Mr. Butz is a natural comic; unlike him, he in no way resembles Franklin Delano Roosevelt.

As Jameson and Benson work together – sometimes as collaborators, sometimes in competition, they encounter love, subplots, and similarities to “The Producers.” The blonde object of their desire is Christine Colgate, whom they take to be a rich heiress ripe for fleecing. (And not just fleecing.) If you saw her in “Debbie Does Dallas” – the stage version, I mean – you know that Sherie Rene Scott is deft comedienne; if you heard her in “The Last Five Years,” you know she’s got some kind of pipes. She puts these gifts together here in a performance that ought to make her a great big star. Next to Ms. Scott’s high, clear, lovely voice, other singers are just gargling.

You can tell it’s a remarkable cast when you get this far in a review without mentioning Joanna Gleason. She plays Muriel, a caustic brunette, who gets some of Mr. Yazbek’s better lyrics: “My prince goes off to war and once again I’m royally screwed. / Perhaps a Xanax and a half will brighten up my mood.”

(Mr. Yazbek pops off another burst of dark comedy in Ms. Gettelfinger’s ode to the joys of Muriel’s home state, Oklahoma. She boasts to Jameson that there’s “Not a tree / Or a Jew / To block the lovely view.”)

All of this silliness unfolds on David Rockwell’s handsome scenery, the well-appointed town of Beaumont-sur-la-Mer. (The set’s hotel and villa architecture improves on “La Cage Aux Folles,” and its seascapes bury “Good Vibrations.”) Mr. Mitchell has choreographed some of the liveliest group dances I can remember from him, and Gregg Barnes’s costumes are fanciful and exact. The lemon-yellow dress that Ms. Scott wears on her entrance is particularly sharp.

So what’s not to like? Not much, at least not in the show itself. The creative team wanted an old-fashioned book musical, and they pretty well succeeded in making one. They even spice up the old formula with some crafty metatheatrics: characters ducking into the audience, self-aware jokes, that sort of thing. Muriel, who appears to leave town at one point, makes an unexpected return. “I can’t imagine I won’t be useful to someone in the second act,” she says.

A show like “Dance of the Vampires” can crash in sulfurous flames without imparting any larger lesson, except maybe that producers, like tractor-trailer drivers, should be required to obtain licenses before they can threaten the public good that way. This show is the reverse: It’s precisely because it works so well that it leaves you with some uncomfortable questions. The whole enterprise of the book musical begins to look musty – a series of conventions that, even when executed pretty well, cease to satisfy. Another slightly forced switch from speech to song? Another extravagant dance? Another bigger-than-big 11 o’clock number? It’s clever, it’s diverting, it’s executed with flair: The only virtue this show doesn’t possess is immediacy, a sense that combining jokes and songs like this is still a good way to capture how the world looks and sounds today.

This is perfect heresy to theatergoers who like their scenery sparkling, their hoofers multitudinous, and their happy endings to come not singly but in battalions. They will find much to enjoy in “Dirty Rotten Scoundrels,” as did I. They will applaud its creators for achieving what they set out to achieve, as do I. They will, no doubt, look forward to more of the same. On that count, they’re on their own.

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