, the latest and maybe the brightest of the aspiring stars in the current wave of Swedish pop phenomena, is only 22 years old, but she's already had an interesting life. Not all that surprising, possibly, since both of her parents are musicians. Her father, Johan Zachrisson, played in a long-running rock-reggae band called Dag Vag, and her mother, Karsti Stiege, was a member of an all-girl '80s punk group called Tant Strul. Well, briefly a member.

"She was a punk for three months," Li says. "It was more of a thing you do when you're young: 'Let's have a punk band!' " Mom soon moved on to photography, and when Lykke was six, the family relocated to Portugal, where they lived in a house in the mountains ("We had a donkey"), and made excursions to India in the winters. Eventually they returned to Stockholm, where Li finished school. Then, at 19, eager to get started on some sort of music career, she moved to New York City — Brooklyn, to be exact, where she shared a dump of an apartment with a fleet of cockroaches.

"I signed up for some improvisation classes, so I could practice my English," she says. "And I did some open-mic nights, and I played in the park, you know? I just partied, I guess."

When her visa ran out, she returned to Stockholm. Her father encouraged her to keep pursuing a music career and hooked her up with an old friend of his, Björn Yttling, then already scoring international hits with the pop trio . Lykke was dubious.

"He produced a lot of indie people — 'I hate myself' kind of music. I didn't know about Peter Björn and John. But I needed somebody to record me. And then we met, and it was a perfect match."

Yttling has co-writing credits on all the songs on Li's debut album, Youth Novels, and his generally minimalist arrangements are a substantial part of the record's charm. Lykke is appreciative of his input.

"He said, 'Sing me some songs,' so I sang with the piano. He said, 'OK, we can work with this — it's not perfect, but it's something we can work with.' It was good. I was writing on my own, and he gave me feedback."

Last year, those sessions produced an EP called Little Bit, the title track of which became a modest hit. She promoted her work on her MySpace page and with a collection of mostly low-tech YouTube videos (two million hits and counting). She also has her own little label, LL Recordings. Life at the moment is very good.

A common assumption about the Swedish music scene — from ABBA in the '70s through such subsequent acts as the Hives, Sahara Hotnights, Jens Lekman and El Perro Del Mar — is that they've all inherited some sort of national pop gene. Li dismisses this — nothing ever comes that easy.

"We don't have a lot of stuff to do in Stockholm," she says. "So you might as well be at home making songs, 'cause there's nothing to do on the streets. But you have to learn; you have to write. You still have to fight for it."