Leah Remini says Jennifer Aniston "couldn't have been sweeter" when she beat her out for a role on Cheers

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Sounds like Jennifer Aniston really is good at making friends.

In Leah Remini‘s new memoir, Troublemaker: Surviving Hollywood and Scientology, the actress says she and Aniston often found themselves reading for the same parts early in their careers – and she couldn’t have been more gracious.

“She was normal, unlike most other actresses, who … would accuse you of trying to ‘psych them out,’ ” Remini, now 45, writes. “So when you find someone, like Jennifer, who isn’t douche-y, you develop a natural camaraderie.”

Remini recounted a time when she and Aniston were both reading for the part of Rhea Perlman‘s daughter on Cheers, and the then-unknown actress seemed genuinely happy for Remini when she got the part – after learning that Remini really needed the income to pay her rent.

“Jennifer couldn’t have been sweeter. ‘Congratulations, honey!’ she said, and I could tell she really meant it,” Remini writes.

For much more from Remini – including her revelations about Tom Cruise, Katie Holmes and more – pick up the latest issue of PEOPLE, on newsstands Friday

The former Scientologist writes in the book that she almost had the chance to work with Aniston – after coming close to landing the role of Monica on Friends.

Remini reiterated the loss when she appeared on The Howard Stern Show Tuesday – and admitted it was tough to watch the sitcom when it ultimately aired and became a smash hit.

“Yeah, I was like, ‘Dammit, my life could have been good right now,’ ” she said.

Remini wrote in the book that she “cried for days” after learning she didn’t get the role, but told Stern it all worked out in the end.

“When you get your show, that’s what King of Queens was for me, that was my part, that was my show, I was meant to have that part,” she said. “You know, then you can look back and go, ‘That wasn’t meant to be,’ but in the moment you can’t pay your rent and your car’s getting repossessed, you’re not happy about it.”