Petra Haden has maintained a friendship with Bill Frisell ever since the acclaimed guitarist introduced himself at one of her shows five years ago.

Imagine her surprise when one day he asked over the phone, “Would you want to do a record together?”

“He said it in this tone like I was going to say no,” Haden said recently. “I almost dropped the phone. I said, ‘Are you kidding? Does the Cookie Monster like cookies? Does a bear shit in the woods? Of course, I’ll do a record with you. Name the time and place.’ ”

Between his busy touring schedule and her juggling of various projects, they found the time and the place and the theme for their aptly titled “Petra Haden and Bill Frisell” (Hear here). Produced by Lee Townsend and released Jan. 11 via Sovereign Artists, the album wraps several original compositions around cover versions of some of their favorite songs.

“We had talked about the different bands that we liked and the different styles – classical, jazz, rock – the whole spectrum,” Haden said. “So we thought we’d do some of our favorite music.”

Their favorites include Elliott Smith’s “Satellite,” Foo Fighters’ “Floaty” (the first single), Coldplay’s “Yellow” and Stevie Wonder’s “I Believe (When I Fall in Love It Will Be Forever).” In a beautifully subtle marriage of Frisell’s lush electric and acoustic guitars and Haden’s sweet voice and signature violin, they also tackle such standards as Henry Mancini’s “Moon River” and George and Ira Gershwin’s “I’ve Got a Crush on You.”

“I couldn’t be happier how it turned out,” Haden said. “Working with Bill was a blast. I keep telling him, ‘We need to play some of this out on the road.’ ”

Until that happens, Haden has plenty on her plate. The former that dog. and Rentals member has taken up friend Mike Watt’s suggestion to do an a capella remake of the entire “The Who Sell Out” album. That disc is out Feb. 22 on Bar/None.

“Mike used to be in the Minutemen. He’s been a family friend since I was little,” Haden said. “He thought it would be something fun for me to do because I like recording a capella stuff. He told me, ‘You should record ‘The Who Sell Out’ the way you do your vocals and the weird harmonies. He said that album had a ton of harmonies.

“He gave me his eight-track cassette player. I would have The Who on the headphones and I would just sing along with it, until I turned it off and started having my own style. I recorded it on cassette with a Radio Shack mike.

“I didn’t know what I was doing. I kept having to call Mike, all embarrassed, like ‘What button do you press if you want to go to track 2?’ He’d have to repeat himself over and over again, but it was a fun experience, even though it took a long time. I started doing it in 2000 or 2001; I just got kind of lazy. I didn’t forget about it; I just got spaced out. I thought ‘Why don’t I just finish this? I could’ve done this in two weeks. C’mon, Petra, life is short.’ ”

Eventually, she would like to take the show on the road, perhaps enlisting a choir to back her up.

“Maybe I could have a choir director help me write the music out,” she said. “All I know is what I hear in my head, so I think I drive everyone crazy because I keep changing things, ‘OK, you do this part. You sing this, and you sing that.’ ”

If two albums in the first quarter of 2005 aren’t enough, Haden says she’s working on a duet-based album and, as one of triplets, she would love to get started on an album with her sisters – billing themselves as The Haden Triplets.

“When I was little, on family vacations we’d all sing in the car,” she said. “We’ve never gotten all our instruments together and played. So I think it’s about time.”

The daughter of legendary jazz bassist Charlie Haden, Petra couldn’t help but be destined for a career in music. But it hasn’t always been easy.

“Ever since I was little, I knew music was my thing,” she said. “I started the violin when I was 8 and I gave it up when I was in high school because I wanted to go to the parties, have crushes on boys and I didn’t think the violin was cool.

“It was something I needed to do, because right after high school, I started playing again. I learned to read music. In high school, I felt kind of lost, that something was missing … it was the violin. But all that time, I kept singing, that’s why I think my main instrument is my voice.”

ON THE WEB: The Petra Haden Shrine.

BWF (before we forget): The Petra Haden album discography – “Imaginaryland” (Win, 1996); “Bella Neurox” Miss Murgatroid and Petra Haden (Win, 1999); “Petra Haden and Bill Frisell” (2005); “Petra Haden Sings: The Who Sell Out” (Bar/None, Feb. 22, 2005).