About 15 minutes into “Gretchen,” I thought: I’m watching this year’s “Napoleon Dynamite.” It has the same quirky vibe, the same small-town characters, quiet tone and semi-absurdist view of high school. The program for the South By Southwest Film Festival compares the title character to a cross between Dawn Wiener from “Welcome to the Dollhouse” and Deb from “Napoleon Dynamite,” and that’s such an accurate description that I won’t even try to come up with a better one.

Gretchen Finkle (Courtney Davis) is a high school misfit. With her long pigtails, pastel sweaters and child’s backpack, she looks like an adult woman playing a little girl playing a high school student. She is ruled by her mother (Becky Ann Baker), never knew her father, and quietly, awkwardly shuffles through her teenage years with cluelessness and pent-up frustration.

When we meet her, she is dating a classmate named Ricky Marichino (John Merriman), a doofy, trashy guy with a mullet and a pot belly who romances her by making obscene sculptures in pottery class. He wants to get to second base with her (at least!), but Gretchen is preserving her chastity. When a slutty girl replaces Gretchen in Ricky’s heart (and pants), Gretchen reacts in a way that gets her sent to the Shady Acres Center for Emotional Growth.

Among the amusing sociopaths and other troubled youths at Shady Acres, Gretchen meets Nick Rangoon (Macon Blair), a bad boy loser who appeals to her the same way Ricky did. When that relationship ends in a similarly alarming fashion, Gretchen goes off in search of her father, Herb (Stephen Root), whom she eventually finds working as a manager in a burger joint.

“Gretchen,” which began life as a short film, is writer/director Steve Collins’ first feature, but it’s a smooth debut, a very confident and funny piece of filmmaking. There’s some Alexander Payne in here (“Election,” “About Schmidt”), notably in the way Collins often shoots Gretchen in close-up, her dim, cow-like features aimed directly at the camera as she contemplates her fate. He achieves some ingenious visual jokes, too, using framing, camera movement and other basic elements to earn laughs that more mundane directors only dream of.

The central performance by Courtney Davis is brilliantly funny, one of those characters who get laughs just by BEING. With her deadpan, perpetually worried face, she looks like a timid version of “24’s” Chloe, always one step behind the rest of the world and slightly off-center.

Gretchen has a very satisfying character arc (which no one in “Napoleon Dynamite” did) as she comes to realize she doesn’t need to settle for jerky men, a decision her mother made long ago. So under all the low-key comedy there’s a little bit of a Girl Power message, too. And if any girl needs to find some power, it’s the lovable weirdo Gretchen Finkle.

A- (1 hr., 37 min.; Not Rated, probably R for brief sexual dialogue, scattered harsh profanity.)