Carly Simon cemented her pop-star status with her third album, 'No Secrets,' released in Nov. 1972. Ironically, Simon wrapped the record's biggest hit, 'You're So Vain,' around what ended up becoming one of rock's most enduring mysteries.

The first single from 'No Secrets,' 'You're So Vain' topped the Billboard charts on Jan. 6, 1973, kicking off a three-week stay at No. 1 and beginning decades of speculation about who Simon was referring to in the lyrics. Of course, songwriters vent about former lovers in their music all the time, but because Simon was known for writing particularly autobiographical songs -- and because she tended to hobnob with the rich and famous -- people really wanted to know who had inspired such withering (yet utterly laid-back) scorn.

One popular guess: Rolling Stones frontman Mick Jagger, who would have made an appealing fit for a number of reasons, among them the fact that he had a glamorous love life to match Simon's (as well as a distractingly fabulous set of lips to rival her own). In addition, Jagger contributed uncredited background vocals during the sessions for 'You're So Vain,' a collaboration Simon said happened simply because "He happened to call at the studio… I said 'We’re doing some backup vocals on a song of mine, why don’t you come down and sing with us?'"

"I didn't take the song as seriously as all that," Simon later reflected in an interview with Uncut Magazine. "It wasn't vengeance -- it wasn't 'Anna Karenina.' It was, 'From this point of view, you don't necessarily look as good as you think you look.' There's not an iota of hate in it. There may be much more of an iota of feeling hurt or rejected... I was definitely a romantic and my hopes were dashed. That led to the song."

While Simon has coyly refused to reveal the identity of her inspiration for decades, she's come out and said it wasn't Jagger (or Warren Beatty, or Kris Kristofferson, or Cat Stevens), and although most of the world still doesn't know for sure who she was singing about, 'You're So Vain' remains a staple of her repertoire. In fact, while she'd go on to arguably greater success with subsequent singles (including 'Nobody Does It Better,' which won an Academy Award), 'Vain' is widely regarded as Simon's signature number.

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