There are rarities that have emerged since his death that I’ve missed, but I remain hopeful. Recently, I caught “À la Françaix,” choreographed in 1951 to music by the French neoclassical composer Jean Françaix. Balanchine left this in his will to Leda Anchutina, widow of André Eglevsky: both husband and wife had been important dancers of his. The Eglevsky Ballet is currently under the supervision of their daughter Marina Eglevsky. The New York Theater Ballet presented it in 2004 and only a very few people in the audience had seen it before.

The Eglevsky Ballet is mainly a Long Island phenomenon. Today, however, other than its annual “Nutcracker” performances (this year there will be a new production), it performs at best intermittently. The performance on Aug. 15 had been scheduled as part of the Morgan Park Summer Music Festival at Glen Cove; a downpour led to its being delayed and moved indoors to the Friends Academy at Locust Valley. And the audience watched the quadruple bill with enthusiasm.

“À la Françaix,” the third item on the program, shows us a flippant side of Balanchine we don’t often see today. Its five characters are (as named in the program) two Sailors, a Flirt, a Dandy and a Sylph. The Flirt does nicely with the Sailors until the Dandy (with handlebar mustache and a tennis racket: the role created by André Eglevsky) strikes her as better fare. The two are dancing promisingly together when along comes the Sylph (dressed in traditional Romantic-ballet attire, soft calf-length dress and floral headdress), who distracts him. He forgets about the Flirt; she even tugs at his trouser leg, but to no avail, and she departs, leaving him with the Sylph.

But you know how it is with sylphs: they come, but then they go. So, after experiencing this alluring little vision of otherness, our Dandy soon returns to the Flirt and starts a pretty duet with her. Sure enough, the Sylph (danced originally by Maria Tallchief) soon reappears. (This actually is the best way to bring any self-respecting sylph back into play.) This time, the Flirt no sooner sees her ethereal rival than she, very funnily giving up the game without a moment’s further ado, droops all over in the Dandy’s arms.

And the Sylph now clinches matters by removing her outer sylph layer. Underneath she’s a bathing beauty in a bright pink mini-dress.

There are no profundities here, but this whimsical story is told with clarity, charm, wit — and just enough seriousness. The duet for the Dandy and the Sylph provides one of ballet’s clearest dance images of mutual attraction between a mortal and an unobtainable creature from another world, as both dance facing each other on one leg and gesturing toward each other, but hop backward as if being pulled apart by destiny.

And there’s just enough humor: the Sylph has a peremptory way of telling him “Come hither!,” never changing her perfect arm position but just flicking her head to nod him to her side. And there’s a nice image of his amorous befuddlement when he’s left on the spot in bourrées (those little string-of-pearls traveling steps that look less foolish when performed by a woman on point).

At every point you can feel Balanchine’s freedom in making new coinage from old currency. In the Dandy’s next solo, he does an entrechat-six (a vertical jump with feet crisscrossing) that lands not with feet together but, with a touch of surprise, apart in second position. And when he returns to partnering the Flirt, she does a series of air turns in his arms, perfectly expressing her excitement at this resurrection of his attentions to her.

Four of these five dancers appeared in other works on the program, and it’s a sign of how well Ms. Eglevsky guards the flame of “À la Françaix” that each of them looked at their best in it. Violeta Angelova (Sylph), Momchil Mladenov (Dandy) and Ted Seymour (a Sailor) all dance with the Suzanne Farrell company;Teele Ude (Flirt) is Estonian. In the other three works — Ms. Eglevsky’s own “Vivaldi” (2001), Balanchine’s “Tarantella” pas de deux (1964) and Kathryn Posin’s “Time 2 Tango” — it was hard to see any particular stylistic cohesion; as you might expect for a once-only performance like this, they looked like pick-up dancers from different backgrounds. But in “À la Françaix” all five were at their most attractive and focused.

The performance of “Tarantella” by Ms. Ude and Vincent Brewer was competent and unremarkable. For those who’ve seen this choreography done with the right explosiveness, this one was merely perky.

I have no quarrel with Ms. Eglevsky’s “Vivaldi” or Ms. Posin’s “Time 2 Tango” except that they aren’t particularly individual or memorable; each makes its dancers look skilled, without foolishness. “Time 2 Tango” is a ballet version of tango nuevo, with high extensions and lifts in which the women’s groins are displayed straight to the audience. It’s not an idiom I admire or enjoy, but, as with the basic elegance of “Vivaldi,” there was enough style for the audience to feel that the music by Astor Piazzolla and Jacob Gade (“Jealousy”) wasn’t being traduced.

Not all of those to whom Balanchine bequeathed his ballets agreed to place them under the guardianship of the Balanchine Trust, which was formed after his death and supervises the vast majority of Balanchine stagings today; and it’s been widely assumed that the three ballets Balanchine left to Ms. Anchutina (the others are the “Sylvia pas de deux” and the “Minkus pas de trois”) are among those few non-Trust works. This would explain why they are so seldom seen. I note, however, that the Eglevsky program says that “À la Françaix” and “Tarantella” are “Courtesy of the Balanchine Trust.” The program was called “Keeping the Vision Alive.” I assume this refers to the Eglevskys’ vision; but in “À La Françaix” Balanchine’s vision was alive too.