NEW YORK, NY.- St. Patrick’s Day is at hand, and that’s why Trinity Irish Dance Company is in from Chicago to perform at the Joyce Theater this week. As Brendan O’Shea, the affable lead singer of the troupe’s house band, joked Tuesday, “They let us in.”

By the time he spoke, the first of nine numbers, not including the band interludes, had already established the basic template. This is Irish dance of high skill — fleet in the feet, starched from the waist up — embodied by a female-dominated group (gender ratio: 17-2) with the precision to speak as one while moving from line to circle to diamond. And all this is modernized with some theatrical lighting (spotlights, red haze) and a goosing of electric guitar.

It’s not “Riverdance” — there’s no New Age hash of Celtic mythology, no cocky male showboating. But the claim of Mark Howard, Trinity’s founding artistic director and principal choreographer, that he anticipated “Riverdance” is bolstered by the inclusion of “Johnny,” a piece he made for “The Tonight Show” in 1991. In stage fog, lasses leap until a sound like Pink Floyd kicks in, and you can watch how a hidebound tradition was scrambling to catch up with the culture around it.

The rest of the selections are much more recent. A voice-over expresses the desire to escape the straitjacket of rules, conformity and overproduced formulas, and the work shows progress toward that goal. Sometimes, it looks like cheerleading without acrobatics, sweetly bland, and Al Crawford’s corny lighting doesn’t help. Even when the dancers are hitting the floor with sticks and supported by a giant lambeg drum, the effect is earnest but underpowered. Yet some of the experimentation has promise.

Best in this sense is “Communion,” which Howard made with Sandy Silva in 2014. The dancers are barefoot, crossing Irish dance with body percussion like that of African American stepping. Here, although I missed the bass — the bottom, the weight — a softness in the approach felt fresh, and the mixing produced some beautiful new spiraling steps, reaching toward a different mood, a different grace.

The show doesn’t stint on traditional pleasures. The band leans toward generic classic rock, but an unamplified folk-based song by O’Shea is a treat, and fiddler Jake James gets the place rocking in the old way. A duet between James and champion dancer Ali Doughty is curious. As the two virtuosos accelerate, she keeps darting on and offstage like a coy fairy; it’s cute but not conducive to musical conversation. After she leaves for good, James comically demonstrates that he can dance, too.

The prowess of the rest of the Trinity dancers is never in question. In “Push,” an exciting series of solos, they show how they push technique: multiplying in-the-air heel clicks to sound like the break at the start of a pool game. But “American Traffic,” by tap-dance choreographers Michelle Dorrance and Melinda Sullivan, ends up exposing limitations.

Typically for Dorrance, the piece begins and ends by isolating the motions of sound production, the shapes made when striking the floor. In this case, the method applies a jeweler’s loupe to one of the foundational glories of Irish dance: the tight crossing of turned-out legs. The middle of the work, though, mixing Irish with tap, magnifies what’s missing. The tap vocabulary establishes that the dancers have functioning hip joints, but they can’t sit into the grooves. They have the rhythmic acuity to walk around clapping in counterpoint or do time steps in canon but not a tap dancer’s charisma and cool.

You can see the same problem in the bows, when the happy dancers try to cut loose under a disco ball. The straitjacket is still on.

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Trinity Irish Dance Company

Through Sunday at the Joyce Theater; joyce.org.

This article originally appeared in The New York Times.