Like any good opening song, the curtain-raiser in “Martin Short: Fame Becomes Me” explains exactly what we’re about to see and why: “Another curtain goes up / On a one-man play / Cause when you can’t book a film / Then it’s hello Broadway!”

If that’s true (and Mr. Short’s credits have tapered off a bit lately), Hollywood’s loss is Broadway’s gain. Mr. Short — the excitable chameleon best known for his work in “Saturday Night Live,” “SCTV,” a string of mediocre film comedies, and more recently “Primetime Glick” — has brought his menagerie of characters to the more hospitable climes of New York.

Director Scott Wittman squanders his talented supporting cast now and then, and the whole thing is encased in a narrative only slightly less belabored than the solo shows it sends up. But Mr. Short’s pinwheeling, almost demonic energy more than papers over any shortcomings. When a 56-year-old man successfully imitates a 16-year-old boy imitating Katharine Hepburn performing her spinning-plate routine, much is forgiven.

Not all of Mr. Short’s creations made the trip East. His Brylcreemed triangle impresario Ed Grimley appears only briefly, and his deliciously oily lawyer Nathan Thurm is nowhere to be found. But fans of the jowly sycophant Jiminy Glick and the Tin Pan Alley tune-slinger Irving Cohen (“Gimme a C, a bouncy C!”) will be in luck. And Jackie Rogers Jr. junkies will pinch themselves as Mr. Short launches into a faux talk show hosted by the albino Rat Packer wannabe.

Mr. Short plays both host and guests in that scene, but a subsequent “Fame Becomes Me” sequence subjects an audience member — sometimes an average Joe or Jane, sometimes a celebrity — to Jiminy Glick’s unctuous attentions. Nathan Lane was the good-natured guinea pig at a recent performance, and seeing this veteran scene-stealer at a loss for words was a rare treat.

With his mildly terrified responses, Mr. Lane amounted to a sixth collaborator for the evening: Daniel Goldfarb, Mr. Wittman, Marc Shaiman, and Alan Zweibel all share credit with Mr. Short for everything spoken and sung on stage. Their contributions include a wide array of topical jokes that range from mainstream (Mel Gibson, Fidel Castro) to defiantly insider (Mandy Patinkin, the 1983 Doug Henning musical “Merlin”).

Perhaps to justify the involvement of so many writers, Mr. Short’s antics have been yoked to a tired framework, an intentionally over-the-top parody of the tales of celebrity angst that fuel shows like “Behind the Music.”

Mr. Short has bought into what I call the Lahr Theorem. This is the notion propounded by John Lahr — New Yorker theater critic and son of “The Wizard of Oz” star Bert Lahr — that the desire and ability to make others laugh stem from psychological scars. (It’s probably no coincidence that Mr. Short’s fraudulently gothic childhood memories include his bibulous father playing a dancing picket fence in an “Oz” knockoff called “The Man in the Moon.” In real life, the elder Short was a steel company executive.)

The authors’ dips into wry sensationalism are occasionally fun but more often musty. Mr. Short has more than enough characters up his sleeve to fill an evening without this device. A less cluttered and more incisive glimpse into his star’s life comes when Nicole Parker, playing Mr. Short’s wife of 25 years, sings about being “Married to Marty”: “Learning how to give a tremendous roar / For a joke you’ve heard him tell 80 times before.”

Here and throughout, the tartly satiric lyrics by Messrs. Shaiman (who also appears onstage) and Wittman outshine Mr. Shaiman’s score. With the exception of the solos “Don’t Wanna Be” and “Glass Half Full,”the songs are more concerned with showing off Mr. Short’s nimble tenor than with augmenting the text.

Mr. Shaiman’s avuncular-imp persona is oddly endearing, but the other four supporting performers are comfortable anytime, anywhere. Capathia Jenkins spends much of the show in the wings, leaving onstage a trio whose verve and versatility would do any production of “Forbidden Broadway” proud: Ms. Parker and Mary Birdsong show off a wide array of terrific impersonations and crisply effective vocals, while Brooks Ashmanskas’s dance breaks are as entertaining as they are superfluous.

Unfortunately, their material has not been well integrated with Mr. Short’s: He’s at his best when they’re out of the way, and vice versa. The ensemble scenes serve to give Mr. Short time to climb into yet another outfit. But some of them, particularly a red-carpet bit with Joan Rivers and Britney Spears, are more padded than Jiminy Glick, which is no mean feat.

But let’s put this in perspective. So “Martin Short: Fame Becomes Me” has a few yawn-worthy patches. So it’s spotty.You know what? Every sketch show is spotty. Go see “Forbidden Broadway” if you don’t believe it. Or “SCTV,” or any episode of “Saturday Night Live.” They’ve all got dead spots .

The trick is to make the highs so high that the mind erases all memory of the lows. And with so many oddball delights to choose from — Mr. Ashmanskas’s Tommy Tune swinging his be-stilted legs like a malevolent giraffe, Jiminy Glick literally falling all over his helpless victim, that ridiculous spinning-plate act — “Martin Short: Fame Becomes Me” comes awfully close to doing just that. Instead of focusing on the snippets that come up short, it’s easy, and far preferable, to let the mind isolate and burnish the many, many barbed, nonsensical, uproarious segments that come up Short.

Open run (242 W. 45th St., between Broadway and Eighth Avenue, 212-239-6200).