Alec Baldwin and his wife Hilaria welcomed a new baby into their lives a couple of weeks ago, and despite some much-needed sleep, they could not be happier about their new addition -- and they've even shared a photo of her already.

“It’s a second chance for me, in a way,” Baldwin told People in their newest issue. “Everybody knows I had a pretty unpleasant custody battle for Ireland.”

New mama Hilaria, for whom this is her first child, explained, "I knew I was going to love her a lot, but it’s incredible how deeply." She added to Extra that in motherhood, "every single day you wake up and it’s Christmas."

Unfortunately, Carmen's sleeping habits are not making things easy for the new parents.

Explained Alec, "She sleeps like a rock all day. And at night she’s like, ‘Let’s have a conference.'"

"Now I’m getting to the point where if I don’t sleep, I’m going to start walking into walls," Hilaria added.

In Hollywood, this is what nannies are for. You can check out baby Carmen in action in a video over on Extra.

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