How Bradley Cooper Transformed Into Leonard Bernstein for Maestro: 5 Hours of Makeup, Years of Research (Exclusive)

Bradley Cooper went to great lengths to resemble famed musical genius Leonard Bernstein in Maestro.

As Bernstein's daughter Jamie, the oldest of his three children, tells PEOPLE in this week's issue, "We had no idea that Bradley had this level of intensity and commitment about a thing when he got it in his grip. There are even certain moments in the film, when he's in motion, where he looks so exactly like our dad it makes us gasp."

Cooper, 48, worked closely with makeup-effects master Kazu Hiro (who won an Oscar for turning Gary Oldman into Winston Churchill in Darkest Hour) to transform into the former conductor and music director of the New York Philharmonic.

Hiro devised four sets of prosthetics and two bodysuits to show Bernstein from the start of his career in 1943 up until his 70s. (He died at 72 in 1990.)

"All in all, I crafted 137 individual pieces, ranging from small to large," Hiro tells PEOPLE.

For Cooper's voice to mimic Bernstein's more nasal-sounding one, Hiro constructed a nose plug the actor wore that changed his intonations and nose shape.

"Bradley's transparency and relentless pursuit of perfection were awe-inspiring," says Hiro.

While Cooper faced criticism early on for the use of a prosthetic nose to play the conductor, who was Jewish, Bernstein's children quickly issued a statement that said they're "perfectly fine" with the makeup, and that "our dad would have been fine with it as well."

Cooper, who also co-wrote and directed Maestro, turned to Oscar-winning costume designer Mark Bridges to outfit his real-life character. Bridges created looks from double-breasted suits to turtlenecks, sometimes recreating outfits from photographs of Bernstein. "He looked so smashing, and if it works, don't fix it," Bridges jokes.

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Throughout the long process of making the film, Cooper kept in constant contact with Bernstein's children — Jamie, 71, Alexander, 68, and Nina, 61 — to ensure he was on track to capturing their father.

"The way he embraced us as he went along in this project — he was so open-hearted," says Jamie. "We wound up feeling like we could trust him."

Maestro, which also stars Carey Mulligan, is in select theaters now before streaming on Netflix Dec. 20.