Lorde is not alone in her selfie-lessness. Several recent big-name acts, including Daft Punk, a pair of Frenchmen whose faces remain obscure despite being the biggest electronic act of the past 15 years, and the Weeknd, a publicity-shy R&B singer from Toronto who initially wouldn’t reveal his identity after his music caught on fire on YouTube, have chosen to take an arm’s-length approach to being famous.

The current incarnation of Fame with a capital F — the white noise of TMZ, endorsement deals for social-media sensations still in high school, and, perhaps, a weariness with celebrity cross-pollinations (who hasn’t Marina Abramovic worked with at this point?) — has arguably become a credibility problem for performers hoping to convey a sense of authenticity and, perhaps more important, sustain some creative longevity. (Even Kanye West hides behind a series of custom Martin Margiela masks throughout the near entirety of his stage time on his current “Yeezus” tour — in an effort, one could surmise, to direct commentary back to his role as an impassioned artiste and away from being better known as Mr. Kardashian.)

“I think if your ambition in making music was to be famous, you’d have something wrong in your head. I’d call it a side effect of making music,” Lorde said. “And I don’t wish I wasn’t well known, but I don’t think it’s something to crave at all. There’s a weird culture now of putting talented people on crazy pedestals, making them these sort of deities, so my relationship with fame is to try and bridge that gap a little.”

Some see a disinclination toward the white-hot spotlight as an intelligent marketing strategy that discreetly helps perpetuate star power nonetheless. “What’s different with Lorde is that her publicity is marketed as anti-publicity,” said Anne Helen Petersen, a professor of film and media studies at Whitman College who recently blogged about the formation of Lorde’s celebrity-noncompliant person. “Here’s a girl who hates manipulation, who exercises meticulous control over her image, and has no qualms about speaking her mind.”

Taking the anti-publicity tour even further is Sia Furler, the Australian singer and songwriter better known simply by her first name. Billboard’s request that she appear on the cover of its Nov. 2 issue was intended to anoint her as an industry titan of Dr. Luke and will.i.am proportions. But Sia had other ideas. In lieu of a traditional portrait, she requested the magazine publish a Banksyish image of her naked from the bust up with a brown paper grocery bag over her head, as well as a 350-word “Anti-Fame Manifesto” that invites the reader to, when thinking of the famous, “imagine the stereotypical highly opinionated, completely uninformed mother-in-law character and apply it to every teenager with a computer in the entire world.”