I’m pretty sure it was pretty big by Cohen and Cales version (the one Jeff would use) and I don’t think it was before Jeff’s death his version really exploded and then subsequently through Shrek did it become everyone’s song.

But Jeff really revitalised the song with hiss masterful voice. Leonard was a master in many areas but his voice wasn’t his big strength.

Fun trivia: In the movie it’s Cales version but on the official soundtrack it’s Rufus Wainwright performing it, who happens to have a child with Cohen’s daughter.