Brandon Routh isn't getting much sleep since becoming a first-time father August 10.

At CBS' PaleyFest event in Beverly Hills September 6, the Partners actor joked that he isn't as well-rested as he looks. "Maybe for this hour and a half I can put on a brave face and then go home and take a nap," Routh laughed while talking to Us Weekly. "All I think of is dreams of diaper changes."

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Though caring for a newborn can be tiring, Routh and his wife, Courtney Ford, are cherishing every moment with their son, Leo James. "Everybody keeps telling me, 'Remember this moment because it goes by so fast,'" the actor said. "'You'll be wishing they were that small again.'"

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Routh, 32, credited his wife, 34, with picking out their son's name. "We'd been looking at names even when we were thinking about having kids. I liked it a lot and it just kept rising to the top of our list," Routh explained. "James is my middle name. Leo's not crazy, it's not out there -- not a lot of Leos."

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When he's not busy shooting Partners with Sophia Bush, 30, Michael Urie, 32, and David Krumholtz, 34, Routh told Us he's keeping track of his baby boy's milestones. "He keeps growing a lot, eating a lot," the actor said. "A lot of diaper changes!"

This article originally appeared on New Dad Brandon Routh: I Dream of "Diaper Changes"