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Warning: this post contains spoilers about Sunday’s episode of “Mad Men.”

Many “Mad Men” cast members have departed over six and a half seasons of that AMC drama, but no one has done it quite like Robert Morse.

In Sunday’s installment, Bertram Cooper, the veteran advertising executive played by Mr. Morse, watches the Apollo 11 moon landing on television and dies soon after – only to reappear in a fantasy witnessed by Don Draper (Jon Hamm), in which Cooper sings and dances along to “The Best Things in Life Are Free,” a vintage show tune from the 1927 musical “Good News.”

The surprise musical number recalls Mr. Morse’s other identity as a song-and-dance man, and a star of the stage and film musical “How to Succeed in Business Without Really Trying.” (He won a Tony Award in 1962 for playing that show’s endearing schemer, J. Pierrepont Finch, in its original Broadway production.)

But Mr. Morse’s extended skill set was one that Matthew Weiner, the “Mad Men” creator, was reluctant to utilize until the actor’s final appearance.

“It was really tough in the first few seasons of the show to not bring it up,” said Mr. Weiner, who wrote Sunday’s episode, “Waterloo,” with Carly Wray. “Bobby has so many gifts, and he played a character who is politically very far from the person that he is.”

“But we did a fund-raiser once where I saw Bobby sing again,” Mr. Weiner continued, “and I saw that he still had it — that boyish charm and everything. I realized that there was an opportunity, in his death, to bring him back in Don’s mind, as a slightly different character.”

As for “The Best Things in Life Are Free,” Mr. Weiner said, “It is a very simple song with a very simple message: Life is bigger than business.”

In an interview on Tuesday, Mr. Morse, 83, spoke about his success on — and departure from — “Mad Men.” These are edited excerpts from that conversation.

Q.

Was it bittersweet for you to leave “Mad Men,” or are you glad to have had such a memorable exit?

A.

I had no idea what I was in for. My phone has been ringing off the hook. And they’re not really hooked anymore. I’ve got an inbox that has been overflowing and Facebook has been going crazy. All I can say is, what a send-off! Exit left, and don’t stop at the door. [laughs] The opportunity to shine in the spotlight that Matt Weiner gave me — it was an absolute love letter. Christmas and New Year’s, all rolled into one.

Q.

But how do you keep that momentum going if you’re not on the show?

A.

I called Matt this morning and I said, how about “Mad Men: The Musical?” [Laughs] Can’t you see it? Bert keeps reappearing, singing and dancing, and sharing his words of wisdom with the team. “Brotherhood of Man” for Roger. “Sit Down, You’re Rockin’ the Boat” for Pete. “Don’t Rain on My Parade” for Joan. “Look to the Rainbow” for Peggy.

Q.

Was it a challenge for you to have spent all this time on a show about a 1960s workplace without ever acknowledging your alter ego of J. Pierrepont Finch?

A.

I was quite elated when Matt called me, and said we’d love you to do this show. He did mention to me at that time that he really remembered me from Broadway and “How to Succeed.” I said I’d be happy to be Bertram Cooper, chairman of the board, and sit behind a desk. It looked like the road company of “How to Succeed.” I remember going down the aisle the first few weeks and singing “A Secretary Is Not a Toy.” And all the girls looked at me — they were very young and most of them didn’t know what the hell I was saying. It was a different age and there’s a few of us left.

Q.

So how did you learn that your time as Bert was coming to an end?

A.

A few weeks ago, Matt said, “Bobby, I’m sorry to tell you but you do pass away.” And I went, “I understand. It’s better to go that way than when you wrote for ‘The Sopranos.'” But he said, “I have an idea that you come back at the end of the show and you see Jon Hamm, and you sing to him.” It served to emphasize the episode’s message, so I was very happy about it. I didn’t want to be, Robert Morse is going to sing a song. I wanted to be Bert Cooper and to keep it very simple.

Q.

How was that musical sequence prepared?

A.

I had a wonderful choreographer, Mary Ann Kellogg, and we worked on it for three or four days, five days, in secrecy. No one was to know, not even my wife or family; no one knew what was going to happen. Nobody knew beforehand. We sang the song three or four times with a 30-piece orchestra, Matt was there. I rehearsed with the dancers and a few days later, Matt came in to see what we had done and said, “It’s going to work.” Then we filmed it in about six or seven hours. I breathed easily and took it easily, as Matt wanted. No great histrionics. Weeks later, I would say to Matt, “I haven’t seen it — is it O.K.?” I was very insecure. “Bobby, I’ve shown it to all the writers and it’s going to be wonderful. Don’t worry about it.”

Q.

And Jon Hamm is watching you as you perform it?

A.

Oh, yes. He was there for me when we filmed the scene. He would be very, very helpful. To see his expression as he watched me, it was wonderful.

Q.

And you’re about to do “In Your Arms,” a new musical work, for Powerhouse Theater at Vassar College — will you be in your full song-and-dance mode?

A.

You probably know more about it than I do. I don’t think it’s that kind of thing. It’s a couple of people on the beach — elderly people — and that’s all I know about it. But I’m going there with an open heart and open arms. I don’t know if I can do 10 shows a week, but going back to Vassar to do this, that’s where I started with “Tru” [for which Mr. Morse won a second Tony Award]. And who knew where we were going, or if it would be all right? And look what happened.

Q.

Is the choreography from “How to Succeed” still locked in your muscle memory? Is it irresistible to break into “I Believe in You” every time you look at yourself in a mirror?

A.

I’ve been often asked to do it, little places here and there. I will say that what’s locked in my memory is Bob Fosse teaching me the dance steps when we were in rehearsal. I wasn’t that fast, and he said, “Go into the other room please, Bobby, with my assistant, and learn it, and then come back in three days, and I will be ready for you, because I’ll have rehearsed all the dancers who will know it before this sentence I’m speaking is over.” That’s how fast dancers are. So I went to see the assistant and learned much of the movement from her. And the assistant’s name was Gwen Verdon. I went: “Gulp.”