Jessica Alba Gives Birth to Baby Girl

Jessica Alba and her husband Cash Warren are new parents.

The 27-year-old actress gave birth to a healthy baby girl, Honor Marie Warren, on June 7, her publicist Brad Cafarelli said June 9 in an e-mail to The Associated Press. Cafarelli didn't provide further details.

Alba and Warren wed last month after becoming engaged in December 2007. They met on the set of the 2005 film "The Fantastic Four," which costarred Alba. Warren was a director's assistant.

JULY 16 UPDATE:

One reason Jessica Alba named her baby daughter Honor was that she felt her own was pretty bland.

"I was always irritated that my name was Jessica," the 27-year-old actress tells OK! magazine. "Come on, it's a very '80s name, because there were tons of Jessicas in every school I went to. There's something great about having a unique name. It's a part of your identity."

She and husband Cash Warren welcomed Honor Marie Warren last month. Alba poses with Honor on the cover of OK!, and all three are featured in a photo spread inside the new issue. The magazine, which recently landed a million-dollar deal with new mom Jamie Lynn Spears, doesn't comment on its pacts with celebrities, though Alba reportedly sold the first shots of Honor to OK! for $1.5 million.

"It's still amazing that she was living inside of Jessica," said Warren, who met Alba on the set of the 2005 film "The Fantastic Four," which costarred Alba as the Invisible Woman and employed Warren as a director's assistant.

Who will be the disciplinarian?

"I think we're pretty even," Alba said. "We're good at communicating and bouncing things off each other. We'll stick to our guns, even when she gives us pout face!"

Warren, however, aims to be the good cop: "I'll hide. Babe, you punish her!"

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