If Baz Luhrmann had his way, the music of the Rolling Stones would have been featured in his 2001 movie, the cult favorite “Moulin Rouge,” alongside David Bowie, Sting and Madonna.

But Mr. Luhrmann couldn’t get the rights .

The film, starring Nicole Kidman and Ewan McGregor, did mighty fine anyway. It grossed $180 million and racked up eight Oscar nominations, including best picture. It spawned a Stones-less soundtrack that went double platinum, and a risqué music video that gave cancan a pop culture makeover. Just try to get through this piece without singing “ Giuchie, giuchie , ya-ya, da-da” to yourself.

Roughly 15 years later, Justin Levine, the 33-year-old music supervisor for the lush new Broadway adaptation of the movie, wanted to try again. He had to solve a creative problem: how the villainous Duke of Monroth, played by Tam Mutu, would meet the heroine, Satine, portrayed here by Karen Olivo .

Mr. Levine made obtaining the rights a personal point of pride. While on a trip to Germany, Mr. Levine set up his GarageBand editing software in a closet and recorded himself singing and playing demos of how the music might be used in the show, before sending them off to the Rolling Stones’ management. Carmen Pavlovic, the production’s lead producer, had already brought on board a former music executive with Stones connections to help with the whole process.