Nicole Kidman says she was engaged to a mystery man in between breaking up with Tom Cruise and marrying Keith Urban. "I didn't really want a relationship," the 40-year-old actress says. "I just wanted my kids to have me, and I didn't feel comfortable having some person in that small hubbub."

"And then I got engaged to somebody ... but it just wasn't right," she continues in Vanity Fair magazine's October issue, on newsstands Sept. 11. "I wasn't ready. We weren't ready."

Details, please.

"I get engaged and I get married — that's my thing," she says, declining to reveal her former fiance's identity. "I don't want to date. I'm interested in a very, very deep connection."

Kidman and Cruise divorced in 2001 after 10 years of marriage. They have two adopted children, Isabella, 14, and Connor, 12; Cruise has a 1-year-old daughter, Suri, with actress-wife Katie Holmes.

Kidman, who married country singer Urban in June 2006, says she has no regrets when it comes to her marriage to Cruise.

"My agents told me, `Once you become Mrs. Tom Cruise, you do know your career is going to die,'" says Kidman, who won an Oscar for her portrayal of Virginia Woolf in 2002's "The Hours."

"I was appalled," she says. "I was like, `Hello? I'm in love, and I don't care if it's shooting myself in the foot. I'd much rather be married and have a family.'"

The couple "lost a baby early on, so that was really very traumatic," she says. "And that's when it came that we would adopt Bella."

Cryptically, she adds: "There's a complicated background to that, given that I never speak much about many things. One day maybe that story will be told."

Kidman hopes to have a baby with Urban.

"I'm yearning to have one," she says. "I think I would be very sad if I wasn't able to have a baby. Keith knows I want one, and he has been getting there slowly."