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Cruise plays the coup's real-life ringleader, the aristocratic Colonel Claus von Stauffenberg.
Suri, often touted as the most powerful tot on the planet, would walk to her dad as he was ready to leave the makeup trailer, and "she would take my eye patch off", Cruise says with his trademark laugh.
"The girls in the makeup trailer got her a stuffed bear with a patch on it so that she would play with that and start to feel very comfortable."
Holed up recently in the Beverly Hills Hotel, Cruise is in the middle of the Valkyrie media tour, which also could be dubbed the "apology" tour, a jaunt with stops at some of the media outlets (Today show, anyone?) that contributed to his famed couch-jumping, Scientology-spouting, psychiatry-bashing media implosion of 2005.
In a green sweater and jeans, Cruise is thin, friendly and solicitous, with practically the only visible sign of age - he's 46 - being the little laugh lines around his eyes.
He also appears relaxed - one suspects that was helped in part by the presence of his wingmen, director Bryan Singer and Singer's childhood friend, Academy Award-winning screenwriter Christopher McQuarrie.
When Cruise is asked if he feels misunderstood, Singer and McQuarrie jump in with the passion of longtime homeboys (well, longtime homies who happen to be intellectual film geeks from Princeton, NJ).
"He's totally misunderstood.
Tom, you need to let us talk about you," says Singer, passionately, as Cruise looks on vaguely embarrassed.
Singer describes the time they all spent with Tom and his family, he and McQuarrie's circle of family and friends in Germany, and in the desert (where they shot a battle sequence).
Says McQuarrie: "He is a really great guy. He's a generous person. He works very hard. He is exceedingly professional.
"There is no hierarchy of any kind on the set. We would have . . . somebody's mother came to visit the set and Tom would spend the afternoon having lunch with that person's mother."
For those who are not Cruise-ologists, here's a recap of the various bad news that afflicted the Cruise world in the past few years.
Besides the various dents to his image, Paramount severed its longtime relationship with the superstar after the so-called underperformance of Mission: Impossible 3.
Cruise rebounded by taking over United Artists, but earlier in 2008, his longtime producing partner, Paula Wagner, left amid charges that the duo was not productive enough.
Their first film, the political drama Lions for Lambs, was perhaps the biggest bomb of his career. Cruise began his image rehab this summer with a hilarious turn as a vulgar studio head in Tropic Thunder and received a Golden Globe nomination for his hip-swivelling.
Still, the task is not yet complete.
A lot rides on Valkyrie, a $US90-million thriller that doesn't exactly shriek good cheer. (Reviews have been mixed to negative.)
The film itself has been dogged with controversy, including the German Government's initial reluctance to let the filmmakers shoot in Berlin's Benderblock because of Cruise's practice of Scientology (a policy later rescinded) and changing release dates.
And, oh yes, Singer, who's made such films as X-Men, is coming off Superman Returns, a blockbuster so ill-received that it conceivably could have killed the franchise.
One can understand why they were happy to retreat to Berlin to discuss the minutiae of the Nazis for hours on end, make a film about brave men banding together to take down the greatest villain of the 20th century and watch a ton of movies together.
"You know we are film geeks," Cruise says.
"And he's worked with every filmmaker that we would be talking about," says Singer, recalling how they would grill Cruise for first-hand dope on greats such as Kubrick and Spielberg.
Singer says he's been obsessed with Nazis from a very young age.
"I had these two friends that were German, and . . . we had a little Nazi club." The kids didn't know what Nazis did exactly, but they were fascinated by the spectacle.
One day, Singer, who is Jewish, arrived home with a homemade swastika armband scrawled in crayon.
"My mom saw it. She, wow, she exploded at the sink. I will never forget [that] and the lecture."
And Valkyrie isn't the first feature film Singer has made about a Nazi - he also directed 1998's Apt Pupil.
As a kid, Cruise himself had "a German helmet that had blood on it". "It was always how we are going to kill the Nazis and how we are going to kill Hitler," he said.
He also liked to watch WW2 documentaries, which left him with a lifelong love of aircraft. (He actually owns a P-47.) "I would look at these images and, of course, I always wondered why didn't someone just shoot Hitler."
Once he started working on Valkyrie, Cruise got what sounds like a personal seminar on Hitler and the Third Reich, led mostly by McQuarrie, who went so far as to interview 91-year-old Rochus Misch, Hitler's last living bodyguard.
Cruise refused to go on that fact-finding mission.
"I didn't want to meet him," Cruise says. "Evil is still evil. I don't care how old you are."
While Singer and McQuarrie led Cruise into an examination of Nazi Germany, he unwittingly also led them into a study of the circus that follows him. "There was some crazy" stuff, says Singer.
Early on, he asked Cruise to come to a coffee shop with him.
And he said Cruise told him, "Yeah, well I can hide. I can lay down in the back of your car. We'll get out [of] the driveway, maybe the people outside the house won't follow". Cruise tries to stay calm, particularly around his kids.
"You just have to accept it. You know you can spend your life living in your single room, but that is not for me. That's not who I am, my family is or how I want to raise my kids.
"I don't want to live that."