STRAIGHT UP.(Emiliana Torrini's performances)

When Emiliana Torrini was sixteen, and working in a caviar factory in a small town near Reykjavik, she asked a friend to help her record five pop and blues covers for her father on his fiftieth birthday. The friend persuaded Torrini to record some more songs--enough to make an album. They released it themselves--as "a joke," she says--and it became the No. 1 record in Iceland, where Torrini, the daughter of an Italian father and an Icelandic mother, grew up. Her subsequent career as a singer and songwriter has unfolded in a similarly fortuitous way. It almost didn't happen at all. In 1998, when she was twenty-one, she moved to London, where, a year later, One Little Indian, an independent British label, released "Love in the Time of Science"--her first album to reach an international audience. Inevitably, she was compared to Bjork, Iceland's most famous (and equally tiny) female singer. A hazy, overblown production, the record situated Torrini's music uncomfortably between Bjork's florid electronic arias and the nameless, oily tracks that you hear in the lobbies of boutique hotels.

In 2000, Torrini's boyfriend died, and she was mugged in broad daylight on a busy London street. For two years, she stopped making music. Then the director Peter Jackson, who had been given a copy of "Love in the Time of Science," invited her to sing "Gollum's Song"--a gothic bit of pap that Torrini's strong, glassy upper register almost saves--on the soundtrack of "Lord of the Rings: The Two Towers."

The experience inspired Torrini to begin work on a new album, "Fisherman's Woman," which came out here in April. While she was recording it, she was hired to write a song for Kylie Minogue, the spunky Australian singer who is ubiquitous in Europe. Torrini and her producer, Dan Carey, wrote the percolating dance number "Slow" in an hour, then repaired to a pub and got drunk. (Many of Torrini's anecdotes involve the words "joke," "accident," and "drunk.") Like Prince's nineteen-eighties hit "Kiss," the most stripped-down dance track ever to become a No. 1 single, "Slow" is audaciously reduced, a sliver of music that pierces the listener like a laser. Carey's electronic track is little more than a teensy drum pattern, a bass line, and a quick keyboard figure that sounds like a sun-dried version of the twinkling arpeggios in Donna Summer's "I Feel Love." Suspended above this skeletal foundation is a melody that unfolds within a single octave and is sung at the volume of a civil phone conversation. Torrini's lyrics tweak the well-worn conceit of the dance-floor seduction, though not so violently that they lose the necessary frankness. The best line is in the second verse, when she elegantly encapsulates what it feels like to meet somebody on the dance floor: "You know what I'm saying, and I haven't said a thing. / Keep the record playing."

Minogue sang "Slow" exactly as Torrini and Carey had recorded it on their demo. In September, 2003, the song went to No. 1 in England, and it earned Torrini more money than any track she has released herself. This is not as it should be. On "Fisherman's Woman," Torrini applies her minimalist algorithm with admirable ruthlessness to the overpopulated genre of mellifluous, well-meaning acoustic music. The album is as intimate and memorable as "Slow," though it sounds more like the morning after the dance, when someone tells you her life story, quietly but quickly, inches from your ear. The songs consist of Torrini's plangent, childlike voice and Carey's incantatory acoustic guitar, occasionally augmented by dashes of piano and subdued drumming. The unexpectedly upbeat single "Heartstopper" is conceived, like many of the songs on the album, as a letter--in this case to a former lover. Torrini sings calmly, able to see the wreckage but : "You said I began this messy state of love affairs. / That I drink too much and smoke too fast, that this city's ...