AvenueQIt’s really puzzling trying to figure out who the producers of “Avenue Q” had in mind for an audience for their puppet show since the production is too coyingly cutesy for grownups and too explicitly sexual for kids. (In fact, the show comes with a warning: “Not Suitable for Children Due to Adult Themes and Puppet Nudity.”)

Yet, for all its marshmallow moments, it’s won all the accolades Broadway can bestow — Tonys in 2004 for Best Musical, Best Score, and Best Book. (Note: I am informed that this production is aimed at people between the ages of 18 and 45 who grew up watching “The Muppets” and would get a kick out of watching them be “naughty.” OK, I’ll buy that.)

The current rendition at the Morgan-Wixson Theatre in Santa Monica is, I suppose, as good as it gets. The puppeteers, wielding the oversized heads of their furry and felt characters, mimic the facial expressions and body language of their Muppet-like stars. After awhile, you can’t tell which of them is real.

The story is simple enough. A new college grad named Princeton (remarkably played by an energetic Aric Martin) moves into a seedy apartment on Avenue Q and proceeds to search for his “purpose in life.” In due course he becomes the lover of a furry “monster” called Kate (Rachel Hirshee), who lives next door and exuberantly joins him in a lengthy, graphic bout of sex. And “puppet nudity” is the least of it.

There is a subplot with a gay Republican (also played by Aric Martin) and the heterosexual object of his affection, Nicky, (Matthew Artson) who only wants to be his friend. There is a pregnant couple, he black (Keith Wright), she Asian (Kristina Reyes), who get married in a Jewish ceremony with “mazel tovs” all around. And there is a female non-puppeteer (Celia Rivera) who inexplicably plays “Diff’rent Strokes” star Gary Coleman. And, finally, there is a hairy Trekkie Monster (Matthew Artson again) who eventually saves the day and helps Princeton find his purpose.

Written by Jeff Whitty, with music and lyrics by Robert Lopez and Jeff Marx, from an original concept by Lopez and Marx, “Avenue Q” was originally intended as children’s television for adults. Director/ puppet master/choreographer Kevin Noonchester steers his artists through their paces in an attractive street scene designed by Thomas Brown. And the story is moved along by the music, which is rendered crisply by the actor/singers — or, if you will, by the puppets.

“Avenue Q” will continue at the comfortable 200-seat Morgan-Wixson Theatre, 2627 Pico Blvd. in Santa Monica, Fridays and Saturdays at 8 p.m. and Sundays at 2 p.m. through April 6. Call (310) 828-7519 for tickets.