"They freaked out. They knew the songs, they liked the arrangements, they stayed with us when we improvised. And I saw I could connect with people using the door of familiarity."

Keyboardist Rachel Z, talking on her cell phone as she walks around her Manhattan SoHo neighborhood, is recalling the audience's reaction at London's Barbican Theatre last May, where she opened for singer Dee Dee Bridgewater before a crowd of 4,000. There, she and her trio gave the first live performance of jazz versions of Joni Mitchell tunes, songs she had just recorded and which were released last fall on the album, "Moon at the Window" (Tone Center).

Since that debut, Z, a jazz-leaning artist who spans genres, having played with both jazz giant Wayne Shorter and progressive rocker Peter Gabriel, has found herself drawing a new audience.

For example, at her performance at Trumpets in Montclair earlier this month, Susie Chankalian, one of Z's friends from the fifth grade at River View School in Denville, came by with her 12-year-old daughter, who read that Z was performing Mitchell material.

"Susie sent me an e-mail, saying that they both really liked the arrangements," says Z, who was born Rachel Nicolazzo in Manhattan and moved to Denville at age 5. "These are people who wouldn't usually listen to jazz."

Z, who shortened her name in the '80s when she was a member of the first-rate jazz/fusion band Steps Ahead, performs with her trio Tuesday and Wednesday at Sweet Rhythm in Greenwich Village. Teaming with bassist Nicki Parrott and drummer Bobbie Rae, Z will offer such well-known Mitchell tunes as "Big Yellow Taxi," "Both Sides Now" and "Help Me" and less-familiar ones like "Lakota" and "Chinese Café" during the first set. Then she'll break off into what she describes as "new standards" for the second, playing numbers by Gabriel, Lennon- McCartney and others.

The Mitchell treatments have a melodic context for the audience and still offer the leader and her partners lots to dig into. For example, "All I Want" is done up-tempo. "That way, we get what we need in terms of a challenging improvised section and the people get a song they know and like which means something in their lives," Z says. "Ladies Man" is another number that was originally slow and is, in Z's hands, done fast. "Big Yellow Taxi" is given a buoyant treatment, says Z, even though the lyric is fairly dark - "They paved paradise/Put up a parking lot."

"Ultimately, the music is light-hearted, so we kept it more straight but with a jazz groove," Z says.

"Chinese Café" is delivered slowly and emotively, as is perhaps Mitchell's best-known number, "Both Sides Now."

The latter song was Z's introduction to Mitchell, when, in kindergarten at River View School, her teacher, Mrs. Windish, had the children sing it. "She also put on pageants twice a year, like doing 'Oklahoma!,' getting little kids to sing and dance," recalls Z, who is a graduate of the New England Conservatory of Music. "She was really hip."

Later, when Z was a student at Morris Knolls High School, she performed Mitchell's tunes at Tavern on the Green and the Greenhouse in Morristown with her friend, Lynne Harrison (now a holistic health specialist who lives in Verona). Z came to see the deeper meanings in the music. "Joni'd get through a relationship, wasn't afraid to reveal her pain and go on," Z says. "I felt I could do the same."

The idea for the Mitchell project came after Z's previous album, 2000's "On the Milky Way Express," which is all Shorter tunes. "I wanted to do another concept album," says Z, who had met Mitchell briefly in the mid-'90s on a visit to her Bel Air, Calif., home with the saxophonist-composer. "And as I was in a singer/songwriter phase myself, I also have a rock band called Peace Box, I started listening to Joni's 'Blue' again and realized I knew all these songs. It became clear what a big influence she'd been in my life."