David Parsons is a whiz at whipping up entertaining dances — with a thick, ingratiating layer of cheese. So it’s a pleasant surprise to see his current show is still entertaining, but with more substance — and less cheddar.

The company’s hometown season, which opened Tuesday at The Joyce, doesn’t rely as heavily on his old standards. His signature piece, “Caught,” is in every show, but the comic hit “The Envelope” will get just one airing, at a matinee on Saturday.

There are two new works, both good. One of them is “A Stray’s Lullaby,” by former company member Katarzyna Skarpetowska, now working with Lar Lubovitch. Her “Lullaby” takes place somewhere in limbo and features two couples barely getting by but not ready to give up.

The foursome moves unsteadily at first to traffic noises that change to scratchy-voiced blues. As the lights change from golden to a smoky haze, one woman dives and claws her way through. Her partner, in suspenders, rushes out fencing, stabbing the air with an imaginary sword. The second couple, a little more buttoned-up in dress, dance together with tender uncertainty, but the piece holds together even in its poignant ambivalence.

Parsons’ new contribution to the evening, “Round My World,” sets three women in blue and three bare-chested men in a circle, moving to atmospheric recorded music by cellist Zoe Keating. In more smoky darkness, they pair off, swirling through four brief sections. The music is lovely and the dance tightly crafted. Even if his ideas don’t last longer than they might in a music video, it’s still the best dance Parsons has made in a while.

It makes a good bookend to the closer, “Swing Shift,” a company staple from 2003. Both use a similar palette of sound, movement and structure with the same swoopy couplings, and the dancers do more moving and less mugging.

Of course, it wouldn’t be a Parsons show without “Caught.” This champion one-trick pony — jumping done with a strobe-light illusion — is now an old mare of 30. Handsome and charismatic Eric Bourne does the leaps that make the piece a hit, but on top of that he dances well. In fact, the company’s nine dancers are particularly good.

Best of all, Parsons holds off on his instinct — at least until the curtain call, when the cast rushes forward, bounding into the air like a chorus line at a dinner theater — to top everything with cheese.