Perry felt confident taking risks on "Prism" because her fans "ended up trusting me at the end of 'Teenage Dream,'" she said. "People have figured out that I'm not going to abuse their attention, so now I think they're ready to jump off with me."
Even so, Perry's label is hardly letting "Prism" market itself.
Beginning in July, when a shiny gold tractor-trailer drove around L.A. with the album's title and release date emblazoned on its side, Capitol Records has kept the singer in public view with performances on the MTV Video Music Awards and "Saturday Night Live" as well as a Citi commercial in which a dad promises his daughter he'll buy her tickets to a Katy Perry concert.
On Tuesday she's set to play a record-release show at Clear Channel Media's new iHeartRadio Theater in Burbank; the next night she'll headline a breast-cancer benefit at the Hollywood Bowl. There's even a fragrance, Killer Queen, that Perry flew to Berlin last month to promote.
"Katy works harder than any female artist I know," said Ellie Goulding, the young English singer who opened for Perry on tour in 2011. "She's handled the enormity of her career and all the weirdness that comes with being famous with immense gracefulness."
One of the label's highest-profile releases this year, "Prism" should have a rollout that feels "pervasive and big and important," said Capitol Chief Executive Steve Barnett. But Greg Thompson, who oversees the company's marketing, insisted the campaign was designed to "pull back the curtain a little bit — to show that Katy is a complex, multidimensional human being."
Asked what he thinks of peeling back the curtain on five more No. 1 singles, Thompson laughed and said, "I love No. 1 singles, and I'm very happy to stock the record with them. But I'm not in control of that — Katy is."
Perry, who said she's involved in every aspect of her business, admitted that she worries about overexposure in the age of social media, especially regarding an album that tries to cultivate a feeling of intimacy.
"You put one thing out and then instantly it's on Facebook! It's on Twitter! It's on Vevo!" she said, punctuating each name with a jab of her hand. "You're like, 'Ugh, just let me make up my own mind.'"
In the wake of her divorce, her love life is something to be handled carefully too. "I never play into the paparazzi," she said. "I don't feed that beast."
That certainly hasn't stopped photographers from snapping pictures of her with her famous boyfriend, John Mayer. (This past summer the singers shared a plush soft-rock duet, "Who You Love," on his "Paradise Valley" album.) "And I put my phone down if I'm going to have a drink," she said. "I don't drink and tweet."
The challenge, she added as she prepared to head into rehearsal, is figuring out what's too much and what's not enough.
"I just want people to see more of me," she said, and by extension less of the "cutesiness" she clung to on "Teenage Dream," when she played shows in an electric-blue wig and a ruffly dress adorned with cupcakes.
"Where can you go from a cartoon character?" Perry asked. "You have to maybe go the other way."