This week Krall releases her fifth CD, the heavenly “When I Look in Your Eyes” (Verve). In addition to her usual trio, Krall is now backed by a lush string section. The result is a richer, more textured sound; yet the orchestra never overpowers the intimacy of her voice. For her new sound, Krall went old school, collaborating with legendary bandleader Johnny Mandel, famous for his work with Frank Sinatra and Barbra Streisand. “He called me up and said, ‘Well, Diana, I just think you’re the sweet spot on the baseball bat’,” Krall says, laughing.

At 34, Krall has carved a unique place for herself in the jazz world. Her arranging skills are sharp and witty; additions, such as the new intro that she and bassist John Clayton worked up for “Pick Yourself Up,” show an increased musical confidence. Her two previous CDs, “All for You: A Tribute to the Nat King Cole Trio” and “Love Scenes,” each spent more than a year at the top of the Billboard charts and each earned Krall a Grammy nomination. “Why Should I Care?” a tune she recorded for the soundtrack to Clint Eastwood’s “True Crime,” is an adult-contemporary radio hit. Says Jessica Sendra, jazz buyer for Borders, “She even sells better than Wynton Marsalis.”

Over lunch at New York’s Union Square Cafe, Krall is dressed in a simple black shirt, pants and dark glasses. On a jazz musician’s clock, the raw oysters she slurps down at 12:30 are actually breakfast. She is as pretty as her early detractors accused her of being, not seeing past her blond hair to the intelligence of her music. Waiting for her entree, she playfully quotes a Fats Waller lyric, “My very good friend, the milkman, says/It would make his burden less/If we both had the same address/So I suggest that you should marry me.” Krall’s sense of humor comes across most clearly in her affection for novelty songs. (Each album includes at least one.) On “Love Scenes,” it was the Blossom Dearie hit “Peel Me a Grape.” On this CD, it’s the sweetly seductive “Popsicle Toes.”

Krall grew up listening to Waller and other classic tunes. Her dad played piano; her grandmother was a singer. “I sound more like my grandmother than anyone,” she says. “She would sing ‘Hard Hearted Hannah’ until the last person went to bed.” Krall began performing, at a local restaurant, at the age of 15. She won a scholarship to the prestigious Berklee College of Music, but quit to play professionally. She recorded two CDs with little fanfare. Then she did “All for You,” a gorgeous set of songs that highlighted her powerful piano playing and her lush, whisky-tinged voice. Just as “All for You” made it to the top of the jazz charts, Krall’s mother was diagnosed with multiple myeloma (a cancer of the bone marrow) and chose to undertake a risky surgery. “I can talk about it now,” says Krall. “This was simply the most devastating thing. Now my mother is well. I’ve just taken my parents to Europe, and I’m taking my father to the White House next week. That’s the best part of my success.”

Krall is sometimes criticized for sticking too closely to the American songbook of jazz. “When Frank Sinatra was recording these tunes, they were old then,” she points out. “They’re interesting to me as a jazz musician, harmonically. I don’t want to be retro at all. Except for Woolworth’s being closed, there’s nothing in these songs that you can’t relate to now.” Even Krall’s clothes defy the retro stereotype. On the new album cover, she wears bright blue Donna Karan. Onstage, she might wear a leather miniskirt. She has a way of injecting irony into her songs that makes them sound anything but old-fashioned. When she sings on this new album, “Oh, do it again/I may say no, no, no, but do it again,” she sounds more like Madonna than Peggy Lee. What makes Krall so interesting is that while she is of the MTV generation, she is cool in a way that the quick cuts of music video can never capture. Like Billie Holiday, she says more with pauses and whispers than she ever says with words.

On June 23 Krall will play her biggest gig yet: headlining at Carnegie Hall. She says her only fear is that she “might trip and fall. Silly stuff.” She’ll do fine. These days, Diana Krall’s got the jazz world on a string.