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Lady Gaga has a new No. 1 song -- on the jazz charts, no less.

"Anything Goes," a version of the Cole Porter standard Gaga and Tony Bennett recorded for their upcoming duets album "Cheek To Cheek," has debuted at No. 1 on the Billboard Jazz Digital songs chart, selling 16,000 downloads in its first week.

Bennett tells us that both he and Gaga are pleased with the song's out-of-the-box success:

"The minute it was released internationally it went right to No. 1 in Billboard. It's thrilling. She's all excited about it. She's always tried to tell everybody she really sings good jazz, and it's on the jazz charts. It went to No. 1... Lady Gaga's a sensational singer. She's a great jazz singer, and this is going to be the first time that people realize she's quite the singer. They're going to be fascinated (by) how well she sings and improvises jazz. She's a great jazz singer."

 The "Cheek To Cheek" album comes out September 23, and Gaga and Bennett have filmed a live performance special that debuts October 24 on PBS's "Great Performances" series.

Bennett says the two are talking about live dates to support the album as well as another project together soon.