Kansas City Ballet must have deliberated long and hard about which works to bring to New York for its week-long season at the Joyce Theater, which opened on Tuesday night.

It opted to show us a representative sample of its repertory rather than cloaking itself in airs of false sophistication. Both artistic director William Whitener’s “First Position (A Reminiscence)” and Donald McKayle’s “Hey-Hay, Going to Kansas City” were made especially for the company, which had performed them for the first time just last month. Artistically, they’re middle-of-the-road; they played well in New York, but probably not as well as they did in Kansas City. Sandwiched between them was Twyla Tharp’s 1980 “Brahms Paganini,” in which Mr. Whitener himself danced a leading role during his years with the Tharp company. Ms. Tharp’s piece gave the evening its intellectual heft.

Mr. Whitener’s “First Position” evokes the French and Danish Romantic ballet of the 19th century, as objectified by a young man who could be a ballet student, but it has some sports orientation as well, as we watch him sometimes drop to the ground in a push-up position. Let’s describe this character as a contemporary and comparatively well-adjusted descendant of the Romantic heroes who went off their heads and uprooted their entire lives after a glimpse of the infinite supplied by sylphids and other supernatural brethren. He was danced Tuesday night by Matthew Powell, who was given a chance to shine in some solo displays of fleet virtuosity.

I call “First Position” middle-of-the-road because it would work as an introduction to this storied repertory for an audience that might recognize its iconography but not be overly familiar with its particulars. But although it was readily accessible, it didn’t pander. It also suggested that Mr. Whitener, who began his career in ballet, might be looking back at his own past. It was performed to Alexander Glazunov in his most beguiling fife-and-drum-and-froth manner.

“Brahms Paganini” opens with a very long solo — no less than 12 minutes — that was strongly fielded by Logan Pachciarz on Tuesday. It recalls Ms. Tharp’s predilection for assigning endurance tests to her dancers, but here it didn’t seem like endurance for the sake of endurance. Ms. Tharp gives us her squiggles, as well as her consistent return to a baseline of balletic verticality, her quivering articulation of isolated body parts, her rippling overlaps between phrases. She breaks up and breaks down her own characteristic syntactic flourishes, rhythms, and articulations so that it’s both classic Tharp as well as something distinctive.

That’s Book 1 of Ms. Tharp’s work. In Book 2, the baton is passed to five new dancers, their asymmetric configuration allowing for a lone woman to gain stature from exclusion. The couples pair off in the style of jitterbugging gymnasts, and there’s a suggestion of the marathon dances of the 1930s. And there are a lot of characteristically hairsbreadth partnering catches and saves and deliberate near-collisions.

“Brahms Paganini” is Ms. Tharp at her best, informed by thoughtfulness as well as showmanship. Lending tartness to it is Ms. Tharp’s ambivalent response to the music; it is there as much to goad her on as anything else, as she attempts and succeeds in matching its pianistic virtuosity with its own kinetic equivalent. In the partnered sections, she even lets her dancers vent some sentiments of Romanticism, but she does so with gritted teeth.

To the question of whether a woman can dance up a storm while wearing a swing coat, dress, and high heels, Mr. McKayle’s “Hey-Hay” gives a resounding “Yes.”

It engages the full company, and the best section was the opening one, in which the dancers made visible the high quality that Mr. McKayle’s formal invention can reach. They are dressed like residents of an unspecified urban environment during the big band years, and the sound track consists of mint jazz selections culled from the University of Missouri’s collection.

After the opening, however, the piece devolves into genre incidents as we visit different joints jumping in different ways. But, while “Hey-Hay” may seem familiar, it leaves audiences pleasantly entertained.