“At a certain point,” Spektor said, staring down at her hands, “if you’re going to become a classical musician, you have to transition. It’s like that speed you have to reach to take off in an airplane. If you don’t hit it, you don’t get up. Then you’re just in a car. I was in a car. And it was torturing me.”

Spektor had been attending Orthodox yeshivas since the family immigrated: first, Salanter Akiba Riverdale Academy, and then the Frisch School, in Paramus, N.J. The summer before her junior year, her piano studies on the wane (“By the end of Frisch, I was already doing a lot less with Sonia. It sort of just trailed off”), Spektor went to Israel with Marsha and other Jewish kids. There, she earned a reputation for making up songs while on hikes. When she returned, Marsha transferred from their yeshiva to high school in Fair Lawn, N.J. Spektor was alone and miserable. Into that void, her new friends from the Israel trip sent cassettes: Joni Mitchell, Ani DiFranco, Tori Amos. Spektor composed her first songs, making bedroom boombox tapes for friends.

“One of the people on the trip,” Spektor told me, “she was coming through New York with her mom and her sister. They asked me to spend the day with them. My friend was saying to her mom, I want Regina to play you some of her songs. And we’re walking through Tudor City, and there’s this bar with a grand piano and no people in it. So I walked in and said, Can I use this piano to play a song for my friends from Florida? So I played a song, and then the maître d’ and the bartender clapped. Then some people came in, and I played another song. And I played another song, and people came out of the kitchen. There was a little crowd, and I said: That’s all I have. The lady who was the maître d’, she gave me her card and said: You’re great, kid. Next time you’re in the city. . . . So I kind of started hanging out with her and her crew. I hadn’t hung out with adults like that before. One night, she called me and said, My friend Andy is a producer and he’s staying at the Four Seasons and just produced Fiona Apple’s record and you should come play for him. So I went and played a few songs for him in the lobby. And he said a You got it, kid kind of a thing.”

Over the next few years, Andy — Andrew Slater, a producer who would become president of Capitol Records — encouraged Spektor. “When I was in high school, I would send little packages to him — cassettes — to his office on Sunset Boulevard. It was like a fantasy. No one in my family knew anybody in the music industry. We didn’t even know a lawyer!”

Eventually, Slater asked Spektor, still in her teens, to move to California so he could get her into a studio and work with her on her songs. She said no. At that point, she was writing five-minute songs. He wanted them to be shorter. “I was very young and stubborn,” Spektor confessed, “that great combination of ignorant and stubborn. When he said: They should be shorter; you should think about structure more, I would bristle so hard. No, I said, I’m not changing my art for anything. I’m doing it how I’m doing it.”

Seven years passed as she waited for the right deal. During that time, she lived at home and worked as a receptionist (“I was on the subway for five hours a day”), then as a caretaker of kids at a social-services center in the Bronx (“I quit because it was just too heartbreaking after a while”). She played downtown clubs, composing 30 to 40 songs a year, recording two records on her own that she sold at gigs, until a showcase at the Knitting Factory led to an introduction to the Strokes’ producer, who offered to work with her. Spektor, then 22, was ready to expand beyond the bare-bones sonics of her records to date, into arrangements that reflected the sounds she heard in her head. As she sings in “Fidelity,” a song that sounds like a pop song about heartbreak, which it is, but which is more truly a song about the heartbreak of hearing songs one can’t quite make others hear: “I got lost in the sounds/I hear in my mind, all these voices/I hear in my mind, all these words/I hear in my mind, all this music/ And it breaks my heart/It breaks my heart.”

On a cold night in late February, Spektor was preparing for a benefit concert in New York for HIAS, the organization that helped her family immigrate. Spektor had bronchitis, and the day before it looked as if she might have to cancel.