The State Ballet of Georgia is a good company, but it can be a lot better still. Its Brooklyn Academy of Music stint, which began on Wednesday night, is the last leg of a national tour, the company’s second over the past year. Since 2004, the company has been led by Georgian ballerina Nina Ananiashvili, who starred with the Bolshoi during the 1980s and 1990s and is currently a ballerina at American Ballet Theatre. Ms. Ananiashvili’s fame is giving the company exposure it might not otherwise have, but the company can stand on its own merits.

The program opened with Balanchine’s “Chaconne,” one of many Balanchine works that the company now performs. Here was none of the hubris that has infected much Balanchine performance in Russia. Instead, the company attempted to perform the Balanchine style accurately, and sometimes tried too hard; the dancers didn’t seem to have acquired any more real ease in his style than they showed last summer at Jacob’s Pillow. Watching them, one is still aware that in every step, Balanchine was asking for an altered rhythm, timing, impetus that makes the step something different than it would be in the standard classical syllabus.

Ms. Ananiashvili herself led the cast. She has been dancing Balanchine works now for two decades, and her experience lends her work an authenticity that is superior to the rest of the ensemble’s. At this point in her career, however, she is also noticeably taxed at times by its demands. On Wednesday she was labored at times, yet overall she performed very well, sometimes beautifully. She never appeared to imitate the role’s creator, Suzanne Farrell, legendary in the Balanchine pantheon.

The live orchestra played the Gluck score well and warmly. And the tempi were not too slow, as they sometimes are when Russian companies perform Balanchine. But a little more musical zest and propulsion would have given an extra push to the dancers.

After an intermission came Balanchine’s “Duo Concertant,” danced by Nino Gogua and Lasha Khozashvili, who share the physical and imaginative space of the ballet with an onstage violist and pianist, here Eric Huebner and Miranda Cuckson. The dancers performed not entirely idiomatically but generously. They were relatively cool when Stravinsky and Balanchine required, but also surrendered to the heart-on-its-sleeve character of some of these quirky series of duets and unexpected separations and reunions. Ms. Gogua extended an admirably magnanimous port de bras down to the ground and upright into the air again.

Choreographically, the Balanchine works towered over the rest of the program, but it was the two non-Balanchine works in which the company seemed most authentic.

Alexei Ratmansky’s “Bizet Variations” received its New York premiere. It is a workmanlike recycling of the vocabulary of what was called dance Impressionism in the Soviet years, which New Yorkers may associate with some of the piano ballets of Jerome Robbins. “Bizet Variations” justifies itself as a vehicle for Ms. Ananiashvili, whose performance here was a highlight of the evening. Though she had to dance shorter and less complicated sequences than she did in “Chaconne,” she gave just as much character running across the stage as she had in the more complex movement of the Balanchine work.

Ms. Ananiashvili dances something of an oddball here. She arrives well after the other two women in the work, and at the end is left alone after vainly trying to follow the rest of the cast offstage. She was flirtatious, enigmatic, integrated one moment, and set apart the next. “Bizet Variations” subtly comments upon her status as dancer and leader within the company.

Following the second intermission, the program closed with “Sagalobeli,” which was also a New York premiere, choreographed by Ms. Ananiashvili’s ex-Bolshoi colleague Yuri Possokhov. The music is traditional Georgian performed live by the Sagalobeli Ensemble. And the choreography is what might be called standard neoclassical ethnography. Juxtapositions of folk dance with ballet are always interesting because the similarities are as numerous as the differences. There was lots of heel-and-toe work for the men, lots of rippling and some effective heel-shuffling for the women. The company was at its most relaxed and most alive in this ballet, and in years to come it may perform Balanchine with the same ease.

Until March 2 (30 Lafayette Ave., Brooklyn, 718-636-4100).