Authenticity is one of Woody Allen’s highest priorities when he shoots his films on location in some of Europe’s greatest cities.

Since being priced out of his native New York, Allen has worked four times in London, once each in Barcelona and Paris, and next in Rome.

He’s a tough but rewarding taskmaster for local crews, who must work out how to balance the very precise vision of his films that Allen brings in his head with the reality of the cities in which he has chosen to set them.

“It’s different for everybody to work with Woody, compared to working with anyone else, but Woody always keeps it the same wherever he shoots,” says his British producer Nicky Kentish Barnes.

Allen stays home in New York for most of pre-production, scrutinizing location and design photos sent by his European teams, and only arrives three weeks before the shoot.

“You keep all the balls in the air until he comes,” Kentish Barnes says.

“He’s written his story, he has the total picture in his mind, and you want to find him exactly what he wants. But he’s also very open, and wherever he goes, he wants it to be authentic. He’s very keen to get the reality of the place, even down to the geography, the reality that a character can get across that particular park in that amount of time.”

That may surprise those local critics who accused him of getting London wrong in his first British movie, “Match Point.” But Kentish Barnes says lessons were learned from that experience.

“We anglicized a lot after ‘Match Point.’ That was his first film fully away from New York, and perhaps we all were not appreciative of the pitfalls.”

Allen always wants to use actual places, whether for exteriors or interiors. His production designer cannot take a shortcut by simply building a set to fit Allen’s script, but must scour the city for the perfect match. Allen also prefers not to travel far to any location.

For his last London film, “You Will Meet a Tall Dark Stranger,” it took nine weeks to find exactly the right apartment overlooking another one, “Rear Window” style — something common in New York, but not in London. When Allen arrived, he nixed the first option, an East End warehouse, because it was the wrong type of building in the wrong part of town.

“He’s tough, but not because he means to be, just because he knows what he wants, and you really want to find it for him,” Kentish Barnes says. “In Barcelona, the house Javier Bardem and Penelope Cruz live in was very difficult to find as well. It’s about getting something that feels right within the country he’s working in.”

Working in Allens favor is the fact that his name opens doors.

“Woody Allen is very respected in Europe,” says Javier Mendez, head of production at Mediapro, the Spanish co-financier of “Vicky Cristina Barcelona,” “You Will Meet a Tall Dark Stranger” and “Midnight in Paris.” “We shot in certain buildings where it is not easy.”

The downside is that his presence tends to draw noisy crowds. “The biggest help the local authorities in Barcelona gave us was to provide policemen to keep people away from the set,” Mendez recalls. “In London, the people are more quiet, but in Paris they went crazy for him.”