from Bill Flanagan's U2 - At the End of the World:
Edge and Larry go off to make some tour rulings and Bono returns his attention to the track-in-progress. A TV monitor has been rolled in and he switches on a sequence from Wim Wender's film-in-progress, a sequel to Wings of Desire to be called Far Away, So Close! The scene is of an angel high above Berlin, looking down and contemplating earth. The angel leaps from his perch, trading divinity for mortality. As we watch, Flood plays back "Sinatra", a moody instrumental track. Bono starts singing along: "Green light, 7-eleven/You stop in for a pack of cigarettes/You don't smoke, don't even want 'em/Check your change."
It's haunting, unfixed and floating. Bono asks what I think and I tell him I think it's real good. He tries out some more lines. He sings, "And if you hit me, I don't mind/'Cause when you hurt me I feel alive." Then he says it might be better if he changed the perspective to: "And if he hits you, you don't mind."
Yeah, I say, that's a lot more concrete. Conversationally the you in the first version sounds like one. Changing it to he hits you makes it vivid. Together with a line that says this victim is "dressed up like a car crash" you're creating a real character. I tell Bono that it makes me think of the only gay kid in a small town. He says he's imagining a woman, not a homosexual, but it's great if it can be read in different ways. He sits on a couch in the control room and sings into a hand-held microphone, leaning forward to put all his emotion into it, squeezing his eyes shut, raising his arm on key lines. Bono singing on the studio couch does not act very different from Bono singing to a football stadium. He tries recording it twice, over two different versions of the backing track, one slow and moody, the other faster and more forceful.
Singing to the harder backing track, he decides that the song is no longer about Wender's angel, so he should change one line of the chorus, which is now, "Stay - as the angel hits the ground." What's a bigger line? He solicits suggestions stopping on "Stay and the night will be enough." He says the song is now strong enough to carry that. He sings the chorus with that phrase, trying it in different spots, from the first line of the chorus to the last. When he sings it as the conclusion, he really makes it a big declaration, raising his right hand in the air and wailing, "Stayyy - and the night will be enough."
Flood is wary of melodrama; it's getting a bit romantic for his tastes. When Bono tries singing, "Stay - with your secrets sleeping rough," Flood puts his foot down. Secrets is one of the words that causes his bathos detector to vibrate. As the song takes on a more grand character Bono makes small adjustments in other lyrics. In order to get in Wender's title he has the line, "Far away, so close, up with the static and the radio waves." He had said "radio waves" in order to be deliberately unromantic, but now that the song's heading the other way, he will drop the word waves and sing the more Van Moorisonish, "Up with the static and the radio."
. . . .
Edge comes in to hear what Bono's accomplished on "Sinatra". He listens, approves, and they fool around with a fade-out melody, ba ba ba-ing it over the ending. . . .
Edge leaves and Bono keeps putting down tracks, changing the lyrics slightly each time. He tells Flood to change the listed title of the song to "Stay," from "Sinatra." Although, he considers, he ought to try to get some reference to Wim's film in there. He decides to call it "Stay (Faraway, So Close!)."