“Joy is a strength; intoxication, a weakness,” wrote the 19th-century Danish choreographer August Bournonville, whose ballets are almost anomalies for their unassuming, unaffected delicacy and charm. In them, feet spring with such elasticity that jumps seem to come out of nowhere; chests open with dignity, not dash; and arms, softly rounded with upturned palms, are like the start of a hug.

Prudence and modesty — increasingly uncommon in today’s culture — are prized in a Bournonville ballet. And even when there isn’t enough space between spectator and stage, and performances have their fair share of opening-night bobbles, watching dancers from the Royal Danish Ballet perform Bournonville’s choreography is an all-too-rare occasion. His ballets have a soothing effect on the soul.

On Tuesday, the Joyce Theater hosted “The Bournonville Legacy,” a program arranged by Ulrik Birkkjaer, a former principal at the Royal Danish Ballet and now a principal at the San Francisco Ballet. The showcase, uneven at times, wasn’t served well by the theater; its intimacy is fine for contemporary ballet, but Bournonville needs more distance, more scope. It was the kind of night in which you couldn’t help flinching at the dancers’ nearness — and holding your breath as you willed them to hold their landings.

The evening began on a tragic note with the second half of “La Sylphide.” In it, James (Mr. Birkkjaer), a young Scotsman, becomes transfixed by a magical sylph (Ida Praetorius) on his wedding day. It doesn’t end well, and ultimately it was the malicious witch, played by Sorella Englund, a former principal dancer who is now a ballet master and coach with the Royal Danish Ballet, who took possession of the stage.