“Listen to me, you’re on a streak,” a drunken Duck Phillips tells Pete Campbell on the penultimate episode of Mad Men. “You’re on one of those — we used to call it a trend. You know, because of the graph, where the line just goes up!”

Mark Moses, the actor who made Duck sauced, is on a streak of his own. Years before his first film credit, Moses acted alongside Sean Penn, Kevin Bacon, and Val Kilmer in the 1983 Broadway debut of John Byrne’s Slab Boys. Penn was coming off Fast Times at Ridgemont High, Bacon was about to land Footloose, and Kilmer was close to Top Secret!, Real Genius, and Top Gun. “I thought, Where’s my ticket? Where do I sign up? How do I get there?” Moses says.

It took him 20 years. The 57-year-old actor, a native New Yorker by way of Evanston, Illinois, broke through a decade ago playing Paul Young on Desperate Housewives — a role he likely wouldn’t have landed if not for a 1990 episode of The Golden Girls written by Desperate Housewives creator Marc Cherry, on which Moses played Blanche’s illegitimate son. Housewives gave way to Mad Men, which in turn led to recurring roles on Manhattan, Homeland, The Killing, and, most recently, TNT drama The Last Ship, which was renewed this month after posting strong ratings in its second season. Moses still isn’t a household name, but he’s achieved the character-actor equivalent: the household face. And in most of his memorable roles, that winning face belies some weakness within.

On The Last Ship, Moses — who in younger days auditioned for “a lot of Kennedys” — is playing his first POTUS, Jeff Michener. Michener’s presidential façade makes him an important player in the show’s postapocalyptic America, but like Moses, he’s taken an indirect route to renown, inheriting the office only after the first 10 officials in the line of succession died in a pandemic. When we meet him, he’s weak-willed and wracked with remorse, in the tradition of Duck and Homeland’s Dennis Boyd.

In a phone conversation last week, we focused on his signature skill: How to be a bad guy with a broadcaster-quality voice and “Just for Men”–model looks.

Your first high-profile part was Lieutenant Wolfe in Platoon, who was sort of a prototype for the roles you’ve played lately.

I met Oliver Stone in New York City. And then I chased him down [in Los Angeles] as the movie got delayed more than once and reminded him that he said I could be in it. And we went back and forth, and I auditioned, whatever he wanted me to do, and finally tried to convince him that I was right for the lieutenant role. I think he had in his mind someone who was really small and would look and appear like someone who would never be a leader, and so they were sort of picked on. And I said, “Well, I think the guy could be a little more all-American like me, where maybe you might believe he could do the job but is actually just totally green behind the ears.” And he finally came around in saying, “OK, you can do it,” and offered me the role when I got off the plane in the Philippines.

Did that disconnect between potential parts and your appearance used to limit the people you were able to play?

It’s funny, I don’t think you have a lot of control over that. I think oftentimes the way an actor looks has a lot to do with how he’s going to be cast. Not always, but often. I had no idea that my career would take a turn about the time of Desperate Housewives, because they weren’t quite sure what that character, Paul Young, would be. The next thing I know, he’s scary and creepy, which we didn’t know. We sort of knew he was going to be slightly menacing or have a secret, but then it became — we latched on to this one aspect of this sinister-type guy. And then I got a series of sinister roles after that — guys that weren’t exactly on the level at times, people that had secrets, oftentimes “bad guys,” they would say. But actually I found a lot of them quite interesting to play. It’s not that you’d want to do that all the time. I’d love to do a comedy right now. But you start getting cast as the heavy all of a sudden, and before that I was doing comedy. Sometimes you don’t know how your career’s going to take you.

So what caused Paul Young to become more sinister?

Well, I’m not saying with all shows — possibly not The Sopranos, maybe David Chase had an absolute, firm idea about who all the characters were in his mind — but a lot of times on new shows, they’re not exactly sure what’s going to happen with the characters, or how they’re going to develop. And then they learn from the actor sometimes, the performance oftentimes, the changes in the script. The interest in the audience tells them sometimes — where do we take this character? And what I thought would be a slightly funny role turned out to be a rather sinister and dark role.

Did your recent heel turn happen because you came to a point in your career where you were prepared to play parts like these, or did it happen because people saw you do it on Desperate Housewives?

Sometimes you get an opportunity with a really good director and you do a really good job. And sometimes you’re given a different opportunity in a lead role, and maybe the role’s not so good or maybe people are just ready for it at different times in their career. That’s hard to be objective about, when it’s yourself and you’re wondering, “Why why why why why?” I had an actor once just walk up to me and say, “What if it never happens?” And I think people wonder that, and they wonder about the risks involved and putting yourself out there, and you always do question whether or not you may have been able to do something better at certain times, or where you were as a person.

It might just be that your career takes a peak when you’re actually ready for it. Someone like J.K. Simmons — he’s been a fine actor his whole life, all of a sudden he wins the Academy Award last year, and you go, “Wow. Why now?” I don’t know, I’m not sure.

What’s the key to conveying these characters’ internal weaknesses despite looking like a family man and an upstanding citizen?

I think the last three, if you talk about Homeland, I think that all spins off of the Duck Phillips character a little bit. It comes from him as this flawed guy who has this terrible weakness that he can’t drink. Other than that, he’s a strong guy. But then once again, it’s fascinating to play a part like that because Matt Weiner would even fool you about Duck. It’s like, “Oh no, Duck’s drinking. Oh wait a second, he’s drinking and he’s even better at what he does. He’s got more balls. How about that?” That’s interesting. Or next you think you’re going to see him in the gutter — he’s not in the gutter, he’s back out there working someplace else. He’s still alive. So it’s full of surprises, and far more gray areas than black-and-white areas, which I appreciated, and I think it made the character. Oftentimes people didn’t like him, especially when I got rid of my dog. But I didn’t write that.

You never know why [actors] do what they do. Some people play superintelligent people, and maybe they always felt like they were stupid. Or they end up doing tough guys like James Cagney, who was a hoofer, because that’s what the audience liked to see him do. So it’s hard to put your finger on why someone is cast or continues to get roles like that. I met an actor named J.T. Walsh years ago, who did a great job in David Mamet’s Glengarry Glen Ross. And I said, “I loved you in this role,” and he turned to me and really was not very happy, and said, “And that’s what I’ve been playing ever since.” So you don’t want to get pigeonholed into stuff.

So being typecast isn’t only an A-list concern? Given the success you’ve had lately, you don’t think about sticking with what works?

That’s never the way I think. I always think of it in terms of reinventing yourself. Whether you’re a writer or a songwriter or anything else, you’re constantly trying to reinvent what you do, and you’re trying to make it better. As opposed to, “I do this really well, and if I can sell this character in a movie, in a film … ” And there are very successful actors out there, names I will not mention, that sell the same slice of chocolate cake in every role they do. And people love to see that. It used to be that way with Hollywood. You’d see a character actor who would do the same thing every time in different roles, but it was always them — it’s always Edward G. Robinson or somebody. And then there are other actors that transform a little more, that might change dialect or this or that or look different.

It depends how the writers see you and believe what you can bring to the role. Sometimes there are breakout roles, like my friend Bryan Cranston got as Walter White. You’ll be going and doing a series for years and you get some recognition from it, and all of a sudden one role comes up and bang. Same thing happened with Jon Hamm. What did Jon Hamm do before Mad Men? I don’t know, some stuff. He did some stuff. We all did. But Mad Men was this decisive, career-changing role. We all kind of hope we get them, and then when you do get them, you’re swamped with so much work you want a break.

How did you get Duck?

I watched the show. I called my agent, I said, “I’ve got to get on this show. If anything comes up on it, send me in.” Something came up the next week. I think I really wanted to be on it because my father, who passed away recently, was on Madison Avenue and led that kind of life. And that’s what I grew up with, so I had an understanding of the characters that embodied that world. I grew up with those guys, they were over for dinner, they were very entertaining guys. Told a lot of jokes, smoked a lot of cigarettes, drank a lot of booze. Were they sympathetic? Yeah, they were sympathetic. Were they idiots sometimes? Yeah, they were all the above. They were complicated people. Many of them with serious cases of alcoholism later on in life. My dad joined AA later in his life. That struck a chord with me, and I talked to Matt about it all the time. Even though I wasn’t on it as much as a series regular, I always felt a deep sense of commitment to that show.

Do you have a favorite Duck line?

I think my favorite line was when [Roger Sterling] introduced me and another guy at a party and said, “Duck, Crab. Crab, Duck.”

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Mine was when you left Pete’s hotel room at the end of the last season, and you turned the wrong way before going the right way down the hall. One of those small, funny-but-meaningful Mad Men moments.

Yeah, and he leans over right before he leaves and says something along the lines of “Take it from me, it doesn’t last very long.” Take advantage of these things, he says, in essence, because they go away fast. And he says it and it’s kind of sad. That’s sort of like Duck. He had it all. He was the big guy, and he lost it. He ends up being a headhunter because no one will hire him anymore. It was sort of bittersweet, and it was a nice send-off for Duck. I’m glad they could bring me back.

Is a moment like that in the script, or does it develop organically?

It’s something you think of or the director thinks of. And I’m not going to tell you who thought of that one. [Laughs.] But it was a good moment. A drunken moment.

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Have you had your own Duck-like moments of weakness or adversity?

I don’t think any actor’s been in the business who hasn’t been fired at some point. And you just go, “Holy shit.” You put your heart and soul into something, and all of a sudden somebody doesn’t want you. And as an actor, it’s hard not to take it personally, because it’s you. You’re the one. It’s not even your story, not even your work. It’s not on paper, it’s you. So I think that everybody’s felt a certain amount of rejection, or those feelings that come about that are hard to understand, whether or not [they’re] being cast right now to play someone with insecurities or betrayal or the deep flaws that go along with somebody like Dennis Boyd.

A script for The Last Ship must read very differently from a Mad Men script.

Yeah, you move the dialogue along and you lay the pipe, you get it going. As an actor, that’s a challenge, because you have to make that interesting. Some people are very good at making this stuff interesting. What they’ve done for 12 or 15 years on CSI, they still come up with the goods and they make it interesting to listen to, because sometimes you’re just like, “Oh, really? Really? Do I have to say all this?”

TNT

What do you look for in new scripts?

I try to look at the potential of the show, and how good the show is. I’d rather have a smaller part in a great show than a large part in a show that doesn’t interest me. Having said that, there’s so much good television out there right now. We really are kind of going through a second golden age of television in terms of the cable networks and Amazon and Netflix and people producing their own shows. There’s just a lot of good writing out there. And it’s a lot of people that are over 40 who can actually do some good writing and not get thrown out of television, which used to happen years ago when there were only three or four networks.

So it’s allowing people to work. It’s allowing good content. It’s allowing shows not to have certain restrictions that happened on the three major networks. And they’re taking chances, and there’s some really good writing. Really, television is an amazing frontier right now. And I love film, I really love film, but so few are coming out that aren’t comic books anymore. And you’re happy to get, in my case, the general in a comic-book movie, because they do so well. But there are just so many comic-book movies.

How have your friends and family reacted to your recent roles?

I’ll put it this way: If you saw Homeland, and you saw the last episode — I went to a Christmas party, and as a gift, they gave me a belt. So that sort of sums it up. They go, “Oh god, I couldn’t stand you, but I loved the show.”

And do you get stopped on the street by people who conflate you and your characters?

I do. Or I get, “Oh my god, you were that guy, oh, I hated you.” They say stuff like that. My kid one time in third grade went to class, and the teacher said, “Your dad’s a murderer.” And he didn’t know what she was talking about. Came home and asked me, and I said, “That’s a television show, and she was kidding. So don’t worry about that, son, I’m not a murderer.”

This interview has been condensed and edited.