Making the role all the more complicated was that Mr. Ledger’s character is meant, in a way, to be a Dylan twice removed. In the movie Mr. Ledger is not playing Dylan per se, but an actor famous, in the fictional world of “I’m Not There,” for portraying Dylan in his early years as a singer-songwriter of protest music.

But because Christian Bale, the actor who plays this early Dylan in the film, was scheduled to film his scenes after Mr. Ledger, Mr. Ledger said he was faced with “playing an actor portraying Christian portraying a Dylanesque character, and not being sure what Christian was going to do.” Or, to put it another way, “Who was I playing when I was acting?”

It all tied him in knots. “I stressed out a little too much,” Mr. Ledger said.

He tends to do that. He is here in London filming the latest episode of the “Batman” franchise, “The Dark Knight.” (Mr. Bale, as it happens, plays Batman; Mr. Ledger plays the Joker.) It is a physically and mentally draining role — his Joker is a “psychopathic, mass-murdering, schizophrenic clown with zero empathy” he said cheerfully — and, as often happens when he throws himself into a part, he is not sleeping much.

“Last week I probably slept an average of two hours a night,” he said. “I couldn’t stop thinking. My body was exhausted, and my mind was still going.” One night he took an Ambien, which failed to work. He took a second one and fell into a stupor, only to wake up an hour later, his mind still racing.

Even as he spoke, Mr. Ledger was hard-pressed to keep still. He got up and poured more coffee. He stepped outside into the courtyard and smoked a cigarette. He shook his hair out from under its hood, put a rubber band around it, took out the rubber band, put on a hat, took off the hat, put the hood back up. He went outside and had another cigarette. Polite and charming, he nonetheless gave off the sense that the last thing he wanted to do was delve deep into himself for public consumption. “It can be a little distressing to have to overintellectualize yourself,” is how he put it, a little apologetically.

Conducting a tour of the house, which he is renting for a few months, he made wry remarks about the art. One painting depicts a crowd of creatures who appear to be in hell, but who seem determined to extract as much sexual pleasure as they can from their eternity of free time; Mr. Ledger has turned another one around and hung it upside down, to no apparent ill advantage.