What is “Royals,” by Lorde, the New Zealand songwriter who performed at Webster Hall on Monday night, doing in the Top 10 alongside Miley Cyrus’s “Wrecking Ball” and Katy Perry’s “Roar”? Most of all, it’s insisting that pop listeners don’t have to settle for clichés.

Ms. Perry and Ms. Cyrus sing about something teenage girls are presumed to have on their minds: what’s left of self-esteem after a breakup. (Dr. Luke, the architect of dozens of hit singles, collaborated on both songs.) Lorde, meanwhile, is singing about class consciousness and conspicuous consumption: the gap between pop-culture fantasies of Cadillacs and diamonds and the reality of being someone who “didn’t come from money.” It’s a thoughtful, calmly insubordinate song; it’s also written by an actual teenager. Lorde, who offstage is Ella Yelich-O’Connor, is 16.

She’s a reflective, even somber young woman. Her set at Webster Hall — the first of three sold-out New York City shows this week — was purposely stark. She wore a demure black dress and was accompanied by only a drummer, a keyboardist and recorded tracks with her multilayered vocals; behind the musicians were spotlights on stands, nothing elaborate. Apart from the backing vocals, which welled up like phantom choirs, her songs were similarly austere: keyboard parts that might be as sparse as a bass line and a chord or two and subdued, unflashy drumbeats.

Nothing hid Lorde’s low, breathy voice, by turns melancholy and resolute. She moved to the beat, but like a teenager, not a music video trouper; her feet sometimes seemed planted to the stage. Lorde wasn’t pretending to be a superhuman pop idol, and her opening song, “Bravado,” confessed to a battle between shyness and show-business aspirations: “I learned not to want/The quiet of the room with no one around to find me out/I want the applause the approval the things that make me go.”