In her dressing room at Conan O’Brien’s late-night show, the 6'8" women’s-basketball wunderkind Brittney Griner is flipping through a rolling rack of men’s shirts with one of her very large hands—they’re bigger than LeBron James’—while also keeping her eyes on the iPhone she’s palming in the other. What attracted the attention of Conan, and the rest of the country, is Griner’s absolute dominance as a college player and her selection as the WNBA’s number one draft pick this spring—in her first pro game, for the Phoenix Mercury, she dunked twice, setting a league record—not to mention the suggestion by Dallas Mavericks owner Mark Cuban that Griner should try out for his team.

Her outfit for her imminent television appearance was settled on a while ago: a blue-and-white seersucker suit with one of her signature bow ties. But backstage at Conan, she’s addressing another wardrobe concern: what to wear to the ESPYs, ESPN’s annual awards show. The event is three days away, and she needs something to wear with the gorgeous black suit that her stylist, Kellen Richards—who’s also Ellen DeGeneres’ fashion adviser—had custom made for her. “With Ellen, we choose women’s clothes and add menswear touches,” says Richards’ assistant, when asked to compare dressing the two women. “With Brittney, it’s all men’s. And it’s edgier.” (The last time she wore a dress, Griner tells me, was at her mother’s request, for her high school graduation. Never again.)

Griner quickly gravitates to a burgundy sleeveless T-shirt by Robert Geller and a black Saint Laurent sweatshirt top with cutoff sleeves and a narrow silver chain sewn across the yoke. Her agent, Lindsay Kagawa Colas, pulls out a Lanvin sleeveless tee with mesh sides as a racier alternative. “Would you like this with no shirt underneath, with nipples out?” she asks matter-of-factly. “That would be sexy,” Griner replies, grinning, “but I don’t think I’m ready for that.”

She retreats into the tiny bathroom to change from her low-slung jeans and Nike T-shirt—the company has signed her to model its menswear, the first time a woman has had that gig—into her suit for Conan. Once the stylist has fussed over her, including rolling her pants cuffs to just the right height, lest they hike up if she crosses her legs—“I never cross my legs,” Griner assures her—Kagawa Colas calls her over for a quick makeup session. “See, it looks like nothing,” she says as she puts the slightest smudge of foundation and undereye concealer on Griner’s smooth, flawless skin. At the WNBA’s rookie orientation, Griner says she declined to participate in a session about makeup application and how to dress. “I don’t need that shit,” she says without rancor, adding that the only lecture she appreciated was one on 401(k)s. (Yes, new WNBA players are taught how to apply makeup while NBA rookies learn to beware of gold-digger groupies who might prick tiny holes in condoms.) Now, peering at herself in the makeup mirror, Griner approves of her agent’s handiwork. “Looks like nothing,” she agrees.