Comic relief, anyone? That’s the invitation of director Alan Paul’s madcap, semi-musicalized “The Comedy of Errors” at the Shakespeare Theatre Company, and the show has a sort of knockabout elegance. Paul honors the mistaken identity plot’s pratfalls and gross jokes, and he has a sturdy cast led by Gregory Wooddell and Veanne Cox, with Cox in particularly delectable form as a lovelorn wife oozing verse and desire.

But “Comedy of Errors” always needs a lot of cranking to get anywhere, and this version is no exception. Is it inspiration or desperation that leads Paul — whose recent staging of “Camelot” is now this troupe’s box-office champ — to weave in so much music, starting with a full-cast opening number about the Greek zest for life?

A tune involving three light-footed cops dancing choreographer Karma Camp’s vintage steps creates a buoyant, devil-may-care air; it’s the most winning of Michael Dansicker’s largely genial original songs. A dirty blues sung by Eleasha Gamble as a sultry concubine in a porcupine get-up — you read that right — is another matter.

That’s the anything-goes atmosphere for the mishaps of a plot involving two sets of twins separated years ago by chance and reunited by the end of the incident-filled night. The show looks like very old comedy with a touch of sprawl, as James Noone’s traditional three-door set revolves to reveal extra locales. This pays off near the end as Paul displays a talent for organized zaniness with characters racing in multiple directions. But this, too, feels like a diversion within a diversion.

The farce is never funnier than when the characters get caught in the confusion and sputter, because what else can they do? Wooddell is Antipholus of Syracuse, a stranger in Ephesus and ignorant that he’s reached his long-lost twin brother’s hometown, and Wooddell’s manic, worried grin is infectious as he gets mistaken for someone with a wife. Christian Conn has less dynamic material as Antipholus of Ephesus, but he fumes with impressive fury as his luck runs the other way.

The same goes for the servant twins, with Carson Elrod getting some of Shakespeare’s friskiest wordplay as Dromio of Syracuse, while Carter Gill absorbs a lot of blows from his masters as Dromio of Ephesus. It’s Cox, though, as Adriana — wife of Antipholus of Ephesus (keep up; you’re doing fine) — who breathes the most life into the language. Cox has a gift for speaking with absurd, glorious extravagance and backing it up with unexpected physicality; she has a dancer’s grace, a classical actor’s aplomb and a nightclub comic’s nerve. You hang on to everything she does because she’s so earnest.

STC veterans Nancy Robinette and Ted van Griethuysen deliver warm turns as older figures with keys to the resolution, and Paul — himself a twin — listens closely to Shakespeare’s themes of doubleness and completion. More slapsticky are the efforts by Tom Story as a jeweler who looks like a creepy swinger, Sarah Marshall as an exorcist sounding like a southern evangelist and J. Bernard Calloway doubling as a majestic duke and an aggressively lusty woman. (There’s a chatty parrot that you’d swear will pay off big, but doesn’t.)

Gabriel Berry’s mid-20th century, mainly black-and-white costumes create a suitable look-alike illusion for the twins; with the big, busy set and the general caliber of the acting, the fashion sense generates an aura of confidence and purpose. Paul, whose work has emerged on the city’s biggest stages, has a showbiz aesthetic that’s refreshing, and his greatest stroke here may be keeping the thing to 100 minutes without an intermission. But it’s a sprint verging on a mad dash, not exactly the more ginger caper he almost concocts.

The Comedy of Errors, by William Shakespeare. Directed by Alan Paul. Lights, Mary Ellen Stebbins; sound design, Christopher Baine; music director, Victor Simonson; fight choreographer, David Leong. With Folami Williams, Matt Zambrano, Matt Bauman, John Cardenas and Justin G. Nelson. About 100 minutes. Through Oct. 28 at the Lansburgh Theatre, 450 7th St. NW. 202-547-1122 or