05/02/2007 AT 04:15 PM EDT
Liev Schreiber, who is expecting his first child with girlfriend Naomi Watts, isn't exactly running out in the middle of the night to buy her pickles and ice cream.
Asked if Watts, 38, has been experiencing any strange cravings, Schreiber, 39, told PEOPLE: "No. She's great. In fact, I've never seen anyone handle a pregnancy so well. She's amazing."
Schreiber was speaking on Wednesday at a Drama Desk Awards nomination reception in New York City (he is nominated for his role in the Broadway revival of Talk Radio
He told PEOPLE he would be with the show through June 24 – because after that, "I'm going to have a baby."
So have he and Watts – a couple since 2005 – been making any special preparations for their impending arrival, such as building a nursery? "Nope," he said. "We're just rollin' with it."
Nor have they selected a name. "We don't know the sex yet," he said.
One thing is for sure: The baby won't be named Liev. "It's an awful name," Schreiber told Conan O'Brien
in February when he first announced that he and Watts were going to be parents. "It's probably the most oft-mispronounced name in showbiz."
Reporting by KARA WARNER