Mr. Weiner said that he was familiar with Ms. Moss’s work from “The West Wing”  she played a presidential daughter, Zoey Bartlet, for seven seasons  but that he didn’t expect what walked into the audition room. “I was shocked at how quickly she metabolized the material,” he said. “She is that kind of actress where we don’t intellectually ever delve into what is going on with her character. It’s almost like it doesn’t pass through Elisabeth’s brain. It’s completely instinctive.

“She works hard, but I think she also works hard to hide it. Either that, or she’s an alien.”

Asked why so many television critics describe her “Mad Men” character as a cipher, Ms. Moss suddenly focuses, answering immediately and aggressively. “I like that they don’t understand Peggy,” she said curtly. “That makes the performance more interesting.”

Suddenly Ms. Moss’s contradictions are starting to make sense.

The third season of “Mad Men” will have its debut on AMC sometime in August. (The cable channel won’t be more specific.) In the first season Ms. Moss’s character concealed a pregnancy, a plotline that required the actress to wear increasing amounts of padding. Season 2 was marked by a big promotion for Peggy and several heart-wrenching monologues for Ms. Moss. What’s next?

“She’s not going to get a sex change, and she’s not going to shoot anybody,” Mr. Weiner said. “You know I’m not going to give that away.”

Ms. Moss didn’t want to give too much away either. Sitting in her living room, decorated with Crate & Barrel furniture, she politely confirmed information but did not elaborate on it. Yes, she practices Scientology. No, she doesn’t collect French Revolution cookware, whatever that is, as some celebrity blogs have invented.

She didn’t want to talk about Fred  too much. “I could talk about Fred for three hours,” she said, fluttering her eyelids and beaming. “But we are very private people.” Ms. Moss met her fiancé, who is 16 years her senior, last October when Jon Hamm, who plays the charismatic Don Draper on “Mad Men,” hosted “Saturday Night Live,” and she joined him for a couple of skits. A date for the wedding has been picked, but no details were forthcoming.