According to U2: Outside Is America (later re-released as U2: The Road to Pop), "Night and Day" was recorded in Edge's basement in the summer of 1990.
"Wild Irish Rose" dates from earlier sessions -- apparently the lyrics originated in 1987 or 88, when Bono was doing some filming in L.A., but it wasn't finished until 1989, when it featured in the 1989 special "Bringing It All Home." (Bono sings from handwritten lyrics, and elsewhere in the interview says that he just finished the song "in the last day".)
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Other sources I've read say 1991 for the TV special. I'm not sure what's right, but notice the lack of the really long sideburns from Edge in the video.
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The music for "Acrobat", according to Bill Flanagan, was written in Australia in 1989. There was a lot of soundcheck jamming around this time, most of it in the very rootsy/Rattle and Hum style. I believe this also led to "Even Better than the Real Thing," which was originally conceived as a Rolling Stones-style rocker, which would make it fit more with where U2 had been than where they were going.
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I read that Even Better than the Real Thing was recorded as a demo called "the real thing" in the same recording session as "Desire". Now would that be the same instrumental demo that's on the Salome outtakes?
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Also according to Flanagan's book, the summer demos from 1990 didn't really go anywhere. I'm guessing Bono and Edge had already worked on "Salome," "Acrobat," "Real Thing," as well as "Sick Puppy" (eventually to morph into "Mysterious Ways") and "Don't Turn Around" (which eventually turned into "Who's Gonna Ride") in those May 1990 sessions. These were probably presented to the band and worked on that summer. When they went to Hansa they had that material, as well as "Blow Your House Down" from the Rattle and Hum sessions (it had originated in 87), and the vestiges of what became "Lady With the Spinning Head" (given how far down the road the backing track for that had gone) and "Until the End of the World". "Take Today" (later to be released as "North and South of the River") also sounds pretty far developed. That's actually a pretty impressive place to start an album with -- five solid songs, and several sketches ("Sick Puppy," "Don't Turn Around," the guitar part for "Until the End of the World"). But it sounds like Adam and Larry weren't all that behind that material ("Sick Puppy" was probably the most confounding), and were impatient when Bono and Edge brought nothing new to the table in Berlin. Not entirely unreasonable either -- you listen to those backing tracks, and they're solid, but not necessarily magic.