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Jonny be good: As Eli Stone, a lawyer with an inoperable brain tumor, Jonny Lee Miller tries to lead a more virtuous life.
Jonny be good: As Eli Stone, a lawyer with an inoperable brain tumor, Jonny Lee Miller tries to lead a more virtuous life.
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Jonny Lee Miller doesn’t want viewers to become sick of him.

The British actor stars as the title character in the new ABC drama “Eli Stone” (Thursday night at 10 on WCVB, Ch. 5) and appears in almost every scene.

“You can’t relax,” Miller said. “You can’t drop the ball for any moment. You can’t get tired. You have to really stay focused. I’ve never really done anything like this for that amount of time.”

His ambition to star on American television was nearly derailed last year. Miller starred in the CBS drama “Smith,” which the network pulled after just two airings.

“Everyone was very excited about ‘Smith,’ and it’s the same thing with ‘Eli Stone,’ ” Miller said. “Now I’m not fatalistic about it. But it’s just that I know not to get overexcited and not to expect certain things to happen.”

Miller was convinced to give prime time another try after he read the “Stone” script about a man with an inoperable brain aneurysm who experiences hallucinations. The role was a marked departure from his parts in such movies as “Trainspotting” and “Aeon Flux.”

“The part was so varied and had such scope to it. This script was something special. An opportunity like that, I wasn’t going to turn my nose up at.”

Leading a show comes with additional responsibilities.

“You have to try not to ever, ever be in a bad mood because it filters down,” he said. “The way the lead actor behaves affects the vibe and the mood of the entire set. It really, really does. I take great care to try to keep it together. I don’t understand when you hear stories of people being difficult or whatever, because it is just not right.”

Miller was Angelina Jolie’s first husband and is the grandson of actor Bernard Lee, “M” in the James Bond movies. He says the validation he got as a child from school productions encouraged him to become a professional actor.

“It wasn’t really a family thing. If you’re a child and you get encouraged to do something and you enjoy it, then that’s it. If you really think about it, I was never going to do anything else.”

Miller plans to run two marathons this year and hopes to someday run the Boston Marathon. Running, he said, gives him energy to tackle his workload. He has discovered he has something in common with his onscreen alter ego.

“I relate to the fact that he’s by no means perfect and (he’s) constantly fighting this selfish streak within him,” Miller said. “He doesn’t become this good guy overnight. He’s still got this spiteful side, and he’s battling that, so I can identify with that a lot.”