NEW YORK — We all know that one song can give singers their career. But can one song help a singer find her voice?

Anjani Thomas thinks so.

Several years ago, the Hawai'i-born vocalist found herself crooning a tune for the most recent Leonard Cohen album. (She had been his backup singer for 14 years, his lover for six). "When I was done with the vocal," she explains, "Leonard said to me, 'Now, could you sing it like you're devastated on a shore with nothing left to give?'

"All my tools went out the window," Thomas says. "I actually was devastated at that point. Then the vocal just came out."

You can hear the results on Thomas' new album, "Blue Alert," a project that gives her rustic and contemplative vocals a rare showcase.

"Blue Alert" combines Thomas' husky voice of hurt and jazzy tunes of woe with entirely new or unrecorded lyrics from Cohen.

Getting the chance to work with Cohen's words is quite a coup. Along with Bob Dylan and Joni Mitchell, Cohen stands among the top troika of lyricists of the past 40 years. His voice, however, is another story. "I'm charitably included in the category of 'singer,' " Cohen explains. "But what I do is really a different kind of activity. Anjani, on the other hand, is flawless. Working with her voice gave me the chance to write in a different way."

Unlike Cohen's more recent work, which has leaned toward political commentary or existential complaint, "Alert" concentrates on the exquisite tortures of love.

Take the title track:

"You know how nights like this begin/The kind of knot your heart gets in/Any way you turn is going to hurt/Blue alert."

While the seeds of the duo's collaboration go back to Cohen's last album, 2004's "Dear Heather," the more intricate mingling of their work developed slowly. Six months after Thomas discovered her new voice (on the Cohen song "Undertow," to be specific), she came across a stray lyric sitting on the bard's desk. "I latched on to the thing — I wanted a shot at it," she says. "I'd never had the temerity to ask for a lyric before. I thought it would be presumptuous. But something came out, and I asked to give it a shot."

Cohen was pleased with the melody Thomas devised for his words, which she turned into the new album's title track. He was also taken with her vocals, which resemble Diana Krall's, only choked by more smoke. Soon Thomas found a discarded version of an old Cohen song, "Closing Time," which included a cache of verses that didn't make the final cut. Thomas turned those verses into the new "Never Got to Love You."

A pattern was set for the collaboration. Thomas wound up rifling through the songwriter's old scraps, finding endless gems to be edited, plundered or expanded on.

According to Cohen, there was plenty to look through. "I have 40 years of journals and napkins," he says. "Maybe we should have called this 'The Napkin Sessions.' "

Thomas cut the songs as the rawest possible demos, mainly with just voice and piano. She had never worked so sparely before.

Born in Honolulu, the singer left the Islands to pursue her career on the Mainland by age 17. After attending Boston's Berklee School of Music, she began playing jazz clubs in New York. It was through producer John Lissauer that Thomas met Cohen in 1984. She has worked with him ever since, singing backup on such albums as "I'm Your Man" and "The Future."

Thomas cut two previous solo albums, one in 2000 that swirled jazz and folk influences with traditional Hawaiian music. The other, in 2001, "The Sacred Names," drew inspiration from various religions' words for God.

Neither bears any relation to the ascetic "Blue Alert." Thomas intended to bulk up the sound on "Alert" before shopping it to labels, and even tried adding a few instruments at one point. But Cohen insisted it was complete. "The space is fully and gracefully occupied by her voice," he explains.

Cohen's label since the '60s, Columbia Records, signed on to release the CD, with him serving as producer.

Fans of the 71-year-old legend will focus on the lyrics. Many of them address aborted love, with full attention on its attendant risks. "They're romantic songs but they do not exclude the consequences of the romantic appetite," Cohen explains. "Love will kill you. But it will also kill you not to go there. Either way, you die."

Cheery stuff. Luckily, there's enough wit and strength in the words and vocals to contextualize the pain. Thomas knows some may still find it rough going. "This isn't something you can dance to," she admits. "But if you give them a chance, these songs can take you to a different world."