Teresa Reichlen performs in George Balanchine’s Serenade. (Paul Kolnik)

Asked about George Balanchine’s ultra-modern ballet “Agon,” Arthur Mitchell once said, “It’s not so much the difficulty of the steps or how flexible you are, it’s the precariousness.”

Anxiety was in the air in 1957, when “Agon” premiered. It was the year “West Side Story” opened on Broadway, with its warring gangs and switchblades; the Cold War was in full swing; and the Ku Klux Klan forced an African American man off an Alabama bridge to his death.

At New York City Ballet, Balanchine cast Mitchell, who is black, and Diana Adams, who was not, in the leading roles of “Agon.” He costumed all of the dancers in simple leotards and tights. In other words, they were nearly naked, and an interracial couple was the centerpiece. Precarious, indeed.

Yet in terms of performance, the tension is an artistic construct, a mood that unsettles intentionally. Internally, the dancers must possess solid confidence if the ballet is to work.

At New York City Ballet’s performance Tuesday at the Kennedy Center Opera House, the precariousness was not an artistic atmosphere; it was a destabilizing presence. The work did not go smoothly, but it wasn’t only the slips and partnering mishaps that confirmed this. Connections among the dancers seemed uneasy.

Amar Ramasar dances in George Balanchine’s “Agon.” (Paul Kolnik/Paul Kolnik)

Balanchine’s choreography, accompanied by Stravinsky’s restless, probing score, resembles a sculptor’s preparatory sketches. It’s a series of investigations that ask: How would it look if the ballerina crooks her leg up behind her and curls it around her partner’s head? What happens if he pulls her foot up, tucks it under his chin and bends her body back so she’s folded into human origami?

Within this slow, quiet experimentation, any miscues and uncertainties are perceptible. Maria Kowroski and Amar Ramasar looked as if they needed more time in the studio together; theirs was not a pairing that inspired trust. You could see it in the way she looked at him, and in the way she didn’t.

“Serenade” and “Symphony in C” were better served — each was radiant, in fact. “Symphony in C,” however, radiated too much, with its Swarovski-crystal-encrusted costumes designed with great fanfare by Marc Happel in 2012. The sparkly effect was striking at first, but then I found it distracting. Reflected light seemed to jump all over the place, assaulting the eye when I wanted to savor the dancing.

Tiler Peck needs no help with illumination; her personality sparkles enough on its own. And paired with Andrew Veyette, her buoyancy lifted the first movement. As much as Peck was focused outward, Sara Mearns turned inward in the second movement. She has a remarkable, complicated presence, at once expansive and remote, and with Jared Angle’s help, she sustained an air of mystery that was especially welcome amid the glitter.

Thankfully, no tinkering has been done to “Serenade.” Clotilde Otranto conducted the New York City Ballet Orchestra in a bright rendition of the Tchaikovsky “Serenade for Strings” (in fact, she lent a vibrant energy to all of the music Tuesday), and the ballet felt new and fresh and deeply moving. Ashley Bouder, Sterling Hyltin and Teresa Reichlen led the cast with charm and authority. Bouder, especially, was magnificent. Her jumps were so high and light that watching her you could feel the air whoosh all around, as if by wings.

New York City Ballet

Through Sunday at the Kennedy Center, 2700 F St. NW. 202-467-4600. kennedy-center.org. Tickets: $25-$109. The company performs the above program again Thursday night and Saturday afternoon. It performs contemporary works Wednesday, Friday and Saturday nights and Sunday afternoon.