Down under the Brooklyn Bridge, near the site of the old Fulton Fish Market, the portable carnival known as Spiegelworld beckons for a third consecutive summer. In two vintage, hand-hewn pavilions known as spiegeltents, two cirque-themed shows are on offer this year: the returning “Absinthe,” a naughty variety-act cabaret that reshuffles its format each season, and the brand-new “Désir,” billed as a cirque show with a through line (à la Cirque du Soleil) about the backstage lives and loves of a collection of 1920s Parisian nightclub performers.

But you’ll have to squint pretty hard to see the outline of a narrative in “Désir,” a loose assemblage of acts that plays more like the B-side of the “Absinthe” record. Yes, there are period costumes (and some much-ballyhooed jewelry from the house of Boucheron), and some abortive attempts at storytelling. But this is essentially another variety show, unified more by its trappings than by any theme or story line.

Any variety show is only as good as its individual acts, and while the acts here never lack for virtuosity — and are made more breathtaking by the setting, a Gosh-they’re-close theater-in-the-round — they’re an uneven lot. You’ll be amazed by the acrobats who stack their hard bodies up to the rafters, and by the ripped “hand-balancer,” who holds his entire body up on one trembling arm. But after such spectacular physical feats, it’s hard to fully engage with the woman flouncing around in a large butterfly costume, the fellow doing Pilates, or the couple performing a watered-down Apache dance.

The Apache dance is one of several times during the evening when the show’s much-hyped eroticism fails to deliver. “Désir” flirts with the transgressive and audacious but won’t commit. So the Apache, who classically echoes a brute encounter between pimp and prostitute, appears here in polite, neutered form. Josephine Baker — whose 1920s Paris “jungle” acts are uncomfortable to watch — is presented as a fresh-faced, winking Hula-hoop dancer. Two expert female aerialists dutifully go through the motions of a staged girl-on-girl flirtation, but you can tell they’d rather be up on the trapeze.

Ironically, the best acts have little to do with eroticism — and everything to do with pacing. Marawa Ibrahim comes out in a skirt made of phallic bananas, fishnets, and heels, but that’s not why her act works. Her set takes flight because Ms. Ibrahim is gifted not only with a phenomenal talent for keeping Hula-hoops aloft — she can spin two dozen of them at once — but with a theatrical flair: She’s a rubber-faced goof with impeccable timing. As she steadily builds her act to a series of ever-higher peaks, she punctuates her feats with delicious expressions: a pursed-lip Betty Boop “ooh,” or a coy flutter of her false eyelashes.

Likewise, the show’s four-man acrobatic team (Nikolay Titov, Nikolay Shaposhnikov, Anton Smirnov, and Evgeny Belyaev) knows how to drive up the tension notch by notch. Acts of formidable strength (pyramids) segue into acts of daring (the first time the smallest acrobat jumps off the human tower, the front row winces). Can the tiniest acrobat do a backflip in midair and land unscathed in his comrades’ hands? He does. And what about a backflip with a full twist? He does that, too. And the double backflip … ?

Wayne Harrison, who directs, clearly understands the value of building to a crescendo, but doesn’t seem to be able to pull the reins tight enough here. Mr. Harrison wants to segue cleanly from the sublime to the ridiculous and back, but the ruthless intimacy of the tiny stage in the round makes for some awkward transitions. One wonders whether the use of an emcee, rather than a chanteuse (Victoria Di Pace), might have improved the flow.

Nor do we get enough of the handiwork of choreographer John “Cha Cha” O’Connell, whose past work includes Baz Luhrmann movies such as “Moulin Rouge” and “Strictly Ballroom.” And after a while, the numbing stretches of world pop chosen by music director Josh Abrahams begin to sap energy from the acts.

All in all, “Désir” feels tentative and a bit unfinished — not a sleek whole, but a collection of segments. Yet for all its flaws, this is the kind of live, intimate cirque show that is rarely on offer in New York. Aficionados of crisp aerial work and acrobatic skill can’t get a better view than the one at Spiegelworld. “Désir” won’t take you backstage at a 1920s Paris nightclub, but it will give you a front-row seat at a virtuoso display of agility and strength.

Until November 2 (Pier 17, South Street Seaport, 212-279-4200).