Paula Abdul and David Letterman have a brief, tense exchange

Paula Abdul and David Letterman had an exchange on "Late Show with David Letterman" Wednesday night that looked like it was about to get nasty. But - SPOILER ALERT - it all resolved with smiles and laughs.

Letterman laid into Abdul about the differences between "The X Factor," Simon Cowell's new show in which Abdul is a judge, and "American Idol."

"It looks just like 'American Idol,'" said Letterman.

"It's so not!" countered Abdul.

"But OK," said Letterman. "How is it not? You have Simon."

"There you go."

"And you," he said.

"Fantastic," said Abdul.

"And a guy who looks exactly like Randy Jackson. How is it not?"

Pictures: The "X Factor" red carpet

Later, Dave said, "You go to church basements and rotary clubs and you get kids out and get grown-ups out and you say, 'OK, dance, sing, we don't care, we'll take you to Hollywood,' right? Am I right about that?"

"I'm not going with that one," said Abdul. At that point, she turned away from Letterman and set her jaw.

He pressed on. "You get them to Hollywood and you have a weekly competition where the audience votes who gets to return. Now how is that not 'American Idol?'?"

"Can I talk? I feel like you're Simon Cowell reincarnated now," said Abdul.

"Ooh, pinch me!" quipped Letterman. Abdul tried to hold back a smile but couldn't. It looks as if she decided to give Dave a break.

"If you'd let me talk for one second, mister, I'll start with the least significant part: A $5 million dollar recording contract."

"So the money's a little better on your show."

"A lot better."

"And they get to sit on Simon Cowell's lap."

"I'll tell you what," said Abdul. "It's not all that it's cracked up to be."

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