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Jennifer Aniston recently mocked her headline-making romances, joking that she wouldn't mind working on "a project titled Everlasting Love with an Adult, Stable Male." Looks like she's doing some very preliminary research: On June 18 she stepped out with Bradley Cooper, the star of the hit comedy The Hangover, for a romantic Italian dinner in New York City. A source says Aniston, 40, spent some of the following weekend with Cooper, but "she is taking it slow" after getting "her feelings very hurt" by her breakup with singer John Mayer this March. "She is in a happy place right now. She is obviously looking for love but is not about to rush into anything."

This isn't the first time the two have flirted. They met at a Hollywood party a few years ago and hit it off, says another source. "They kissed that night and have seen each other a few times [since]." Cooper, 34, saw Aniston earlier this year while doing publicity for their movie He's Just Not That Into You (they didn't share any scenes) and snuck into her Management premiere on May 5, setting off a flurry of dating rumors that even got the attention of Cooper's mother. "My mom loves it!" Cooper told PEOPLE, though he denied any romance with Aniston at the time. "I am single," he said.

But Cooper isn't one to kiss and tell. A Philadelphia native and Georgetown University grad, "he's a very mellow and cool guy," says a neighbor in Venice, Calif., where the actor enjoys surfing and walking his dogs. Now that Aniston has started filming the comedy Bounty Hunter in Atlantic City, what does the future hold for them? For now, says a source, "they are just flirty friends with a lot of chemistry and curiosity between them."

  • Contributors:
  • Reporting by Pernilla Cedenheim / Los Angeles,
  • Alyssa Shelasky / New York City.

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5 Things to Know About Bradley
1 HE GOT COZY WITH CAMERON DIAZ They stepped out in '07. Small dating pool? Diaz and Aniston also both went out with John Mayer and Paul Sculfor.

2 HE WAS MARRIED FOR FOUR MONTHS Cooper married Jennifer Esposito in 2006 only to file for divorce four months later. "I want a partner who is supportive, and I haven't had that," Esposito said after the split.

3 HE CAN COOK He didn't just star in Kitchen Confidential. "I'm an awesome simple cook," he says. "I take after my grandmother."

4 HE LOVES DOGS Like Aniston, he has two: Samson and Charlotte. "They are both rescue dogs, and they are the best," he says. "I cherish them."

5 HE'S A LADIES' MAN The actor has been spotted hanging with Mary-Kate Olsen, Lake Bell and Rhona Mitra.