While recording her latest album, Modern Cool, last January, jazz singer and pianist Patricia Barber just wasn’t satisfied with Dave Douglas’s trumpet solo on her tune “Silent Partner.”

Undeterred, Barber explained to him how the girl in this song felt “waiting in a hotel room” for her secret lover. Douglas hit it on the next try.

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Barber, 43, decided some years ago that she needs to run the show–and it’s starting to look like she’s right. Modern Cool, released at the end of June, sold 35,000 copies in its first six months, despite being distributed by a Chicago independent label that had done only five other records. Good sales for a jazz album start at 25,000–Herbie Hancock’s high-profile Gershwin’s World, which debuted at number one on the Billboard jazz chart this fall, has sold just 74,000 copies, according to SoundScan.

Much of the critical attention for Modern Cool has focused on Barber’s lyrics, which are both beautifully intelligent and decidedly sensual. As the San Francisco Chronicle put it, Barber combines “the poetic songwriting approach of Joni Mitchell and the sophisticated jazz of Bill Evans.” Nine of the dozen tunes on Modern Cool are originals.

Barber pulls the late shift nearly every Sunday night at the Green Mill, 4802 N. Broadway, duetting with her longtime bassist, Michael Arnopol, and on Mondays they play the same venue with drummer Eric Montzka. This weekend she’ll play two gigs with a quintet that also includes guitarist John McLean and percussionist Ruben Alvarez, including one that’s free: a promotional gig Friday at 6 at Borders Books & Music, 830 N. Michigan. The group will then headline at the Green Mill Saturday at 8. Call the Green Mill at 773-878-5552 or Borders at 312-573-0564 for more information. Barber’s also part of the “Women Who Swing” showcase at the Old Town School of Folk Music, Sunday at 6:30; see Neil Tesser’s Critic’s Choice in Section Three for more info. –Mara Tapp