It hasn’t been especially feted during the lead-up to David Letterman’s retirement, but one of the bravest things the Late Show host aired during his 22-year tenure was Perfume Genius’s network-television debut in 2014. Clad in a black PVC bondage harness beneath a blinding-white suit and wearing scarlet lipstick, the artist otherwise known as Mike Hadreas sang “Queen”, from his just-released Too Bright album, backing up lines like “No family is safe when I sashay” with snake-hipped dancing and a provocative stare.

Perhaps the best thing about the performance, though, was the look of utter disbelief Hadreas allowed himself just before the cameras went elsewhere, suggesting that viewers weren’t the only ones thinking “What the hell was that?”

“When they told me I was going to do that show, I was really excited, but I was also completely terrified,” Hadreas recalls, in a telephone interview from his Everett, Washington, home. “I’d never done anything like that before, so I had a lot of time to be nervous about it—and after it was done I kind of had a sober blackout. That happens to me a lot when I’m nervous: I’m like, ‘I did something, but I don’t really remember what I just did.’ ”

Getting a call from Letterman’s office is just one of the many surprising things that have happened to Hadreas of late, although making Too Bright was perhaps the biggest shock of all. The new record’s 11 short, enigmatic songs suggest that he’s abandoned narrative for incantation, and he doesn’t disagree.

“With the first two albums I wrote a lot more patiently, and I suppose I was sort of mining my history for material,” he says. “This album, a lot of the lyrics are a lot more improvised—and written with the music, as opposed to kind of plotting out the words after I had a few chords, or the opposite. It’s a little less mathematical.

“I don’t dismiss anything I’ve written, and I still enjoy writing the way I did for the first two albums,” he continues. “But I felt kind of limited by it, in some ways. Basically, I was trying to write that exact same way, and nothing good was coming, so I had to shake it up in whatever way I could.”

Producers Adrian Utley, of Portishead fame, and Ali Chant can take some credit for Too Bright’s electropop-meets-glam-rock sound, but a pair of powerful women—one otherworldly, the other unreal—helped Hadreas reinvent himself. The avant-garde soprano Diamanda Galas, he says, inspired him to explore the higher end of his vocal range and the more theatrical side of his nature.

“She’s really close to whatever she’s tapping into for inspiration, and it’s almost… Well, it is scary, and I love that,” he explains. “I think I love that she’s Greek, too.…I’m Greek, and I love to see other weird Greeks.”

As for his other source of distaff inspiration, Hadreas has a confession to make. “I have this kind of alter ego on Facebook, this woman who posts these really insane status updates,” he says. “It’s kind of ridiculous, but I’ve noticed that if I write as her for a while then eventually my brain unlocks and I can start writing my own music.”

Frank though this sounds, Hadreas is not quite ready to let his fans be her friends. “She’s so crazy I don’t know if I want to be officially connected with her,” he adds. “And it’s just going to sound crazier and crazier the more I try to explain it, so I’m going to keep it as private as possible.”

Is letting this much out an act of genius, perfumed or otherwise? Probably not, but it’s a rare misstep from an artist who’s clearly growing into his name.

Perfume Genius plays the Imperial on Thursday (May 21).