In the surprisingly winning comedy “Bad Moms,” stressed-out Amy Mitchell (Mila Kunis) launches a campaign for PTA president. She’s sick of bake sales, sick of making breakfast, sick of micromanaging her family. Amy’s bold campaign speech to a group of exhausted women: “If I’m elected, I promise you — we are going to do way less.”

It’s the opposite of what you might expect from a female politician, and in this movie it strikes a rousing populist chord. These women already have it all. What they’d like is to give some of it up.

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“Bad Moms,” written and directed by Jon Lucas and Scott Moore, of “The Hangover,” is designed to sell that movie’s libidinous humor to a female demographic. What’s impressive is how far it rises above its mandate. Yes, there are sexual jokes and drunken pratfalls, but “Bad Moms” isn’t about a crazy misadventure. It’s a smart, sweet, even sensitive comedy about three female Howard Beales who decide they’re mad as hell and not going to take it anymore.

The story is built around Amy, mother of two spoiled kids (Emjay Anthony and Oona Laurence), wife of a couch potato (David Walton) and underpaid employee at a hip startup (Clark Duke is perfect as her millennial boss). After bonding with two misfits — an endearing Kristen Bell as doormat Kiki and a show-stealing Kathryn Hahn as slovenly Carla — Amy decides to run against PTA despot Gwendolyn (Christina Applegate, better used than she has been in years). The terrific support cast includes Annie Mumolo, Wanda Sykes and Jay Hernandez (as Jesse, “the hot widower”).

How did Lucas and Moore, who portrayed women as mirthless nags or sexual fantasies in “The Hangover,” suddenly develop such a keen feminine touch? Often they simply hand the reins to their stars — all working mothers in real life — who improvise their way through some very funny speeches about children, husbands and sex. Built into the script, though, is a distinctively female sense of dissatisfaction. Whether Lucas and Moore are being insightful or just shrewd, it works.

The title of “Bad Moms” may convey rebellion, but it also conveys how these women feel inside and becomes a rallying cry for Amy’s PTA revolution. “You can’t quit,” Kiki tells Amy at a crucial moment. “Quitting is for dads!”