May 21, 2015 5:56 AM EDT


The comedy thriller Spy, in theaters June 5, boasts laugh-out-loud performances from Oscar nominees Melissa McCarthy and Jude Law, a bracingly funny turn from action superstar Jason Statham and an unexpected extended cameo from the rapper 50 Cent, playing himself. But the film’s true star is Rose Byrne’s hair.

Byrne, 35, plays Raina Boyanov, a ruthless Bulgarian heiress; she’s the primary antagonist to McCarthy’s Susan Cooper, a frumpy CIA desk agent who heads into the field to stop Boyanov from selling a nuclear weapon to a terrorist organization. Clad in tacky-expensive catsuits with layers of spectacularly coiffured extensions, Byrne looks like–as Cooper jokes–“a slutty dolphin trainer.”

“My hair needs its own credit,” Byrne says. “I would be [in hair and makeup] for an hour and a half, but I’d always have to go back in because it would start to melt into different shapes on my head. It’s part Marie Antoinette, part Eastern European, part Kardashian.” Still, it’s to Byrne’s credit that she wears the hair–the hair never wears her.

For the Australian actress, it’s the latest in a recent run of performances as a comedic powerhouse. A Sydney native, Byrne first made waves stateside starring opposite Glenn Close on the 2007 legal thriller Damages, which earned her a pair of Emmy nominations and marked her as one of the stars of the new golden era of scripted television. “I feel lucky because Damages was part of that renaissance,” Byrne says. “It’s not the bastard child of the business, as it once was.”

But as Damages wound down, concluding in 2012 after a five-season run, Byrne turned her attention to a big-screen crossover. A key role in the blockbuster Bridesmaids saw her stealing scenes as Helen, a scheming bridesmaid who goes head to head with Kristen Wiig; in Neighbors, she was every bit as irresponsible in her efforts to oust the raucous fraternity next door as her husband, played by Seth Rogen, was. Byrne’s willingness to risk being unlikable ends up earning her the biggest laughs.

Byrne recently banded together with a coterie of Australian actors to launch the Dollhouse Collective, an all-female production company that works to develop projects with more-complex roles for women. In that, she joins the likes of Reese Witherspoon–who produced last year’s Oscar-nominated films Gone Girl and Wild–and other performers working to rectify the dearth of female-driven movies in Hollywood. “It’s endlessly frustrating–the representation of women, and the limitations that are placed on roles, especially in commercial films,” Byrne says.

That issue of representation is what makes Spy so clever: it works as an impressively choreographed action film and as a brash, crass comedy–two genres that appeal predominantly to men. But it also functions as a nifty little piece of feminist messaging. The CIA dresses McCarthy’s Cooper in dowdy disguises for fieldwork–“I look like someone’s homophobic aunt,” Cooper moans–but she ends up being a shockingly capable undercover agent. Likewise, Byrne’s Boyanov is an atypical antagonist, delivering withering put-downs and offing her henchmen with a panache that’s winsome.

Byrne credits director Paul Feig, who also helmed Bridesmaids, for the film’s empowering slant. “Paul’s done so much for women in the business,” she says. “He’s broken every convention.” By populating the world of Spy with fresh, surprising characters–like Boyanov, a properly nasty and nefarious villainess, and Cooper, a worthy successor to James Bond in the unlikeliest package–he upends the viewer’s expectations of how women are supposed to look and behave. “The joke’s on us,” Byrne says. “Everybody has that prejudice against women. He’s making people rethink that.” Even when those women have really bad hair.

This appears in the June 01, 2015 issue of TIME.

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