There was originally another story set in New York where Bardem and Chris Rock played lovers, but when Sally Potter was editing the movie, and admittedly much to her dismay, she didn't feel it clicked with the rest of the movie so she cut out those scenes.
After the closing titles, there is a title card that says "For Nic Potter". Nic Potter was a British bassist and composer. He is also the younger brother of director Sally Potter , and he passed away in January 2013 at the age of 61. The last two years of his life, Sally was Nic's caregiver as Nic was battling with dementia.
Elle Fanning previously worked with Sally Potter on Ginger and Rosa as the title character Ginger.