Fiona Apple showed up late for an interview with her excuse on a makeshift leash. It was a black-and-white wire-haired mongrel that had been abandoned in the New York subway. Ms. Apple and her manager, Andrew Slater, were walking through Central Park when they came across some policemen offering the dog to passers-by as an alternative to the city pound.

"It's an adult dog and no one's going to take it and it would be done away with," Ms. Apple said in a nervous rush. "I feel like it's your fault if you know something might happen to that dog and you don't do something. That dog never did anything to anybody. And I would have been sitting here wondering." 

Ms. Apple, clearly, is a worrier. In her songs, she broods about guilt and responsibility, agonizing over why love goes wrong and who sabotaged the latest liaison. She's buffeted by her own passion and insecurity and tormented by people who take advantage of her or suddenly turn indifferent. 

In the songs on her two albums -- her second one is due for release on Tuesday -- she ricochets from anger to self-laceration, from bitter memories to tentative promises. Her second album brings new complexities: shifting, metamorphosing music that shadows ever more unsettled relationships. 

While her publicist called People for the Ethical Treatment of Animals about placing the dog, Ms. Apple settled on a couch at her publicist's office to talk. She was voluble and fidgety, putting on and pulling off a pair of gloves while she spoke about music and fretted about the dog.

Since she lives in Los Angeles, she would be unable to take it home herself. Partway through the interview, a woman arrived from the animal rights group (for whom Ms. Apple has recorded public service announcements) with a leash and an assurance that the dog would live. 

Ms. Apple, now 22, started working on her first album, "Tidal," when she was 17. Its songs, including the 1996 hit single "Criminal," pondered the desires and choices that arrive with adolescence. When the album appeared, Ms. Apple was praised for frankness and mocked for self-absorption. By the time she was old enough to vote, it had sold two million copies. 

She didn't hold herself back. In interviews she revealed that one song, "Sullen Girl," was about getting raped when she was 12, and she mentioned her years of psychotherapy, her fears and her compulsive rituals. When she received the MTV Video Music Award for best new artist in 1997, she blurted out a speech that concluded, "It's just very stupid that I'm in this world."

While nominees who were carrying their thank-you's on index cards rolled their eyes, the diatribe made Ms. Apple seem earnestly unpolished, an arty high school girl who had somehow landed in show business.

Yet her gawkiness ended at her music. Ms. Apple's sultry voice and troubled phrasing gave her songs a precocious gravity. So did her piano-centered melodies, harking back to standards and blues.

While other musicians her age were learning basic guitar chords or techniques of sampling as the 1990s began, Ms. Apple immersed herself for a year in "The Real Book," a collection of Tin Pan Alley songs, to teach herself jazz harmony after she gave up classical piano lessons. 

The title of the new album (Clean Slate/Epic 69195) hands new evidence to those who consider Ms. Apple self-indulgent. It's a 90-word pep talk: "When the Pawn Hits the Conflicts He Thinks Like a King/What He Knows Throws the Blows When He Goes to the Fight/And He'll Win the Whole Thing 'fore He Enters the Ring/There's No Body to Batter When Your Mind Is Your Might/So When You Go Solo, You Hold Your Own Hand/And Remember That Depth Is the Greatest of Heights/And if You Know Where You Stand, Then You Know Where to Land/And if You Fall It Won't Matter, Cuz You'll Know That You're Right.'

The screed, she said, was sparked by a derisive story and letters about her in Spin magazine. "I was crying, like, 'This can't be happening,"' she said. "'People are personally attacking me way too much, and I need to remember that I do everything for the right reasons.' I question my motives, I make myself proud, I am a good person, I've never done anything to hurt anyone, and this is not me that they're putting down. This is something that they've created. 

"I needed to write something, the same way that I write songs, when I feel like I need to clarify something to make myself feel better. I didn't have a piano because I was on a bus, so I wrote a poem. And then I figured, I'm going to get into a lot of this stuff again where I'm probably going to get attacked a lot. To remind myself, I'll just make it the title."

On the new album, her bravado rises and ebbs, song by song. The word "crazy" keeps turning up; she applies it to herself, but she also lashes out at someone who uses it to keep her weak and dependent. "Call me crazy, hold me down, make me cry, get off now, baby" she snarls in "Limp." But in "Paper Bag" she admits, "I know I'm a mess he don't want to clean up."

Crazy or not, she won't be dismissed. "When the Pawn ... " shows increasing musical confidence, a willingness to let songs crack open or take odd turns while her voice grows tender or vehement. She growls, lets loose elaborate melismas, works up to near-sobs or spits out bursts of words; her voice quivers and breaks with suppressed fury. 

Orchestral passages and strange keyboard sounds slip in behind the piano, bass and drums, and the late-1960s Beatles seem to hover on the sidelines of Jon Brion's production, spurring Ms. Apple to try the extra chord change or let another instrument poke through. 

Like the music, the romances in Ms. Apple's songs are increasingly unstable. Ms. Apple is still mulling over what happens when a lover decides to be just friends and she's still enmeshed in intimate power games. This time, however, she's enveloped in contradictions and ambivalence.

Her lyrics, as the album title suggests, aren't graceful reading; they're made to be sung. "You're all I need," she insists in the album's opening song, with her voice growing more heated as she repeats the line. But she can't convince even herself: "Baby, say that it's all gonna be all right/I believe that it isn't," she concludes.

She knows she's not blameless; "Fast as You Can," her new single, signals its mood swings -- love me, fight me, don't go, get out while you can -- with tempo changes and unlikely interludes, from a blunt hip-hop drumbeat to flutelike "Strawberry Fields" keyboards. 

In "To Your Love," she apologizes to people she's driven away. But in other songs, like "Get Gone" and "The Way Things Are," she sees all too clearly that she ought to escape a relationship yet can't force herself to break free. 

"I haven't learned those lessons," Ms. Apple said. "I mean, I've learned them, but I'm not done with them. But at least it's a step to write it down."

"When the Pawn ..." is an album of fascinating solipsism; while the lyrics wrangle, the music seems to understand every flip-flop. The combination of painful, sometimes clumsy honesty and punctilious craftsmanship makes Ms. Apple sound as if she's growing up on the spot.

And she may be starting to enjoy the process, traumas and all. "I'm gonna make a mistake, I'm gonna do it on purpose," she sings in "A Mistake," over a taunting guitar lick. "And if you wanna make sense, whatcha looking at me for?"

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