In the thoughtful, affectionate “Stinkers,” I counted the characters and arrived at eight — which is weird, because I’m usually good at math in the single-digit range, but the correct total is six.

Two are puppets, operated by two human actors, and the four are so vivid that I counted them all. The puppet design, the naturalness of the humans’ response to them and the puppeteers’ skill encourage us to keep shifting our attention between the puppets, which enact the physical behavior of a pair of toddlers, and the actors, who perform the facial expressions and speech that puppets can’t.

Long story short: The idea of a comedy about a family in which the kids are puppets sounds like it could be really terrible. In fact, it is the best thing in Josh Tobiessen’s play, getting its world premiere at the Jungle Theater.

Chelsea M. Warren’s beautiful puppets are different enough from an actual 3-year-old boy and 20-month-old girl that they require us to help create the characters. Between them, our imaginations and the skill of Reed Sigmund and Megan M. Burns, who play Oscar and Evie, we collaborate to dream up two children who seem astonishingly real. It took a couple minutes to get used to it but, very quickly, I was sold on Burns’ barely verbal Evie and Sigmund’s Oscar, whom Sigmund vocalizes in two registers: whispery soft and VERY VERY LOUD, with nothing in between.

The children are crucial to “Stinkers,” which I’d argue is about how the tiniest people in a family tackle the huge task of teaching their parents how to be parents. As inconvenient as Oscar and Evie are when they need a fight adjudicated or a snack, and as cluttered as Warren’s set is with their toys and diapers, the children are the best-adjusted people on stage. They are honest (Oscar, as adults babble: “This is boring to me”), compassionate and bright, which speaks to the skills of their calm father, Brad (John Catron, wryly underplaying the straight role in a play full of large personalities).

Brad, who raises Oscar and Evie while their never-seen mother works elsewhere, was not so lucky in the mom department. Sally Wingert has played many mothers but none remotely like her Type A Joyce. She is fresh out of jail for a white-collar crime, and it is immediately apparent that whatever success Brad has had as a parent was not from modeling Joyce but from reacting against her (“I raised you, didn’t I?” she asks, to which comes his reply, “Kinda.”). It’s also apparent that Joyce and an associate (George Keller, in a performance as economical as it is funny) are pulling a scam. Complications ensue, and Josh Tobiessen’s elegantly structured play unfolds them with as much logic as is possible in a house ruled by toddlers and an unscrupulous ex-con.

“Stinkers” is big-hearted and droll but what I like most about it is its untidiness. I didn’t respond to a bro, played by Nate Cheeseman (he seems like an unlikely friend for Brad), but he’s typical of the way “Stinkers” is willing to upend its plot when the messy lives of its characters intervene. The play is full of surprises, which makes moments like the final tableau linger in your mind. Joyce, who has barely had time for the kids, finally takes notice of them, leaving us with a corollary to the truism that you never stop being a parent: It’s never too late to become a good one.