NYTB/Chamber Works has so much going for it. Known up until very recently as New York Theater Ballet, it has, for more than 40 years, maintained high standards as a scrappy, chamber-size troupe in the big city. Its hard-working, unaffected dancers have been presenting repertory gems and worthwhile curios overlooked by major troupes, alongside new works by choreographers sometimes also unjustly neglected by the big guns.

Since 2015, the company has had a congenial home at St. Mark’s Church, where its programs, like the current one, always featuring live music and musical interludes, have some of the warmth and intimacy of recitals in a college town. It’s an atmosphere of gently rising expectations, which can be pleasing but unstable. A standout dancer or an especially good premiere can stoke desires for more than the company can reliably deliver, casting the troupe’s modest virtues in the unflattering light of discontent.

This should all make Stravinsky’s “The Soldier’s Tale” a resonant choice for the troupe. The 1918 theatrical work is a fable about a soldier who trades his violin — his soul — to the devil for wealth, only to realize the true happiness he’s given away. More than once, he loses something precious by grasping for more. And that’s the moral stated in the text: “You can’t have everything.”

The new production that had its premiere on Thursday boasts direction and choreography by Robert La Fosse, whose pedigree as a performer includes both New York City Ballet and American Ballet Theater. For a soldier, it has Stephen Hanna — who left City Ballet for Broadway — and for a devil, the celebrated performance artist John Kelly.