My favourite unreleased R.E.M. song is called “Night Swim” (maybe?). The file I have of it sources it as an “Out of Time” outtake, though it was not included on the reissue for that one. It does not sound anything like “Nightswimming”, but is a melancholy guitar-based instrumental with Michael riffing over it (I don’ think he sings actual words.)
As you can imagine the name makes it quite difficult to Google. Can anyone provide me with any further information whatsoever about this hidden gem?
Hello! I was thinking about this exact thing the other day. [Insert spiderman meme]
I has it on a cassette version of OOT demos/outtakes from back in the late 90s. It has long left my collection and was surprised it wasn’t on the anniversary set. From what i remember, you are correct in that it sounded nothing like Nightswimming.
Here it is:
I have it on tape somewhere, too, but YT was easier. 
Sounds like it contributed to the evolution of Imitation if Life, imho.
The YouTube-comments have some insights, linking it to “It’s a Free World, Baby” (don’t really hear it) and the theory that this a first attempt to the “Nightswimming”-lyrics (seems unlikely, as I remember reading the music always came first for them).
“Nightswimming” was, apparently, one of the exceptions to the music-first rule. According to the story, Michael had the lyrics and Peter and Mike were “competing” to write music for them. That being said, I don’t know if this piece of music was in contention or the title “Night Swim” was just arbitrarily assigned to it for the bootleg (I think it had a different title on one of the other bootlegs of this material). In any event, a great tune and one I wish they had finished and released.
I liked it but it sounded like so many other songs mixed together I can’t even pick one! Well I guess Pretty Persuasion and Gardening at Night are a couple 
the bridge in that song at 1:40 that has the same chord progression as “it’s a free world baby”
Mike Mills has disputed the “songwriting competition” story about “Nightswimming.” As he remembers it, Stipe did not have the lyrics in advance, but heard Mills messing around with the music that would become “Nightswimming,” and only then wrote the words.
Live and learn, I guess. Thanks!
In fairness, neither he nor Stipe have precise, encyclopedic memories of these things. I recall Mills saying in an interview a few years ago that REM didn’t carry material from prior recording sessions into new albums. The reality is that most of their albums include songs that were demoed from prior album sessions.
From what I could understand so far about the story of the creation of “Nightswimming” (bits and pieces everywhere along the years, so no, I have no idea where I read about it), both Stipe’s lyrics and Mills’s piano tune already existed, apart from each other and unbeknownst to one another, and were then matched when Michael heard Mills playing it and then adapted on top a poem he had already written about nightswimming. This would be unusual in terms of their collective songwriting process because the lyrics already existed and were just adapted to fit.
Of the composition of “Nightswimming,” in the interview “Automatic Track by Track” for Radio X, R.E.M. - Automatic For The People Track-by-Track | X-Posure | Radio X - YouTube, Mills said,
““Apparently, Peter wrote in some liner notes [for In Time] that it was a competition to see who could write songs for those lyrics, and I don’t remember it being that way at all, it was just something I was messing around with, because it’s really fun to play, and I would just sit down and the piano and goof around with it, and Michael heard it and said, ‘Keep playing that,’ so I did, and he started coming up with really beautiful stuff for it, and before long it was a song.”
As with the story of all the words for “Man on the Moon” being written at the last possible second, or of “Country Feedback” being written and recorded in one take, Buck’s oft-repeated story of the songwriting contest to set Stipe’s poem/lyrics for “Nightswimming” to music likely isn’t true. At the very least, his story and Mills’s story can’t both be true. As you note, people’s memories are not perfect, especially when they’ve lived lives as full of incident as the members of R.E.M. have. But there’s also pretty clearly a pattern of stretching the truth and gilding the lily, exacerbated by getting away with doing so for decades, as gullible journalists simply print whatever tall tales they are fed.
Mills has pretty consistently refuted some of the stories told by Peter and Michael, as when he fairly recently denied Stipe’s claim, from the Rolling Stone cover story on Monster, if I recall correctly, that the band briefly broke up during the final sessions for that album.
I don’t see the competition part being necessarily true, and I fully agree their memories can be seriously damaged – just as a recent example, Stipe stated that “E-bow” was a letter written to Patti Smith, when it was clearly written for River Phoenix, as exhaustively stated back in the day.
But I do think that both music and lyrics were their own things apart (I read somewhere that it was indeed a poem already written by Stipe when he heard Mills playing) and were then matched to build the song. That, at least, wouldn’t be a stretch or gilding the lilly.
Like most lyricists, Stipe had a notebook of lyrics and song ideas. To him tell it, when he heard Berry (or Buck?) messing around on the mandolin with what became “Hairshirt,” he said, “I’ve got words for that.” I wouldn’t doubt it if he already had some of the idea for the lyrics of “Nightswimming” written down in his notebook when he heard Mills messing around on the piano. But, in Mills’s memory, Mills had no idea that those lyrics existed, nor did he write the music for “Nightswimming” to fit those lyrics. If Mills’s memory is accurate, Buck’s oft-repeated “songwriting competition” story cannot also be true.
As with most stories to good to be true - see also the “Stipe wrote all of the lyrics for ‘Man on the Moon’ on the last day of mixing, sang it once, while we all stood there dumbfounded” story - when something seems to good to be true, it likely isn’t true.
Can we maybe agree that
a) It would be a lot to ask of any prolific songwriter to always remember the creative process behind every song they’ve ever written in all its gory detail?
b) Neither Michael nor Peter have ever been known for letting the truth get in the way of a good story?
c) On a cosmic scale it matters fuck all?
Cos all of those are true. Just saying. Feck’s sake!
Mills pretty clearly has the worst memory of the four - when David Buckley interviewed him for Fiction, he couldn’t remember which hit singles were on which albums, which, as you note, isn’t that surprising. However, what Mills does remember usually tends to be more accurate and realistic than the tall tales spun by Peter and Michael. One gets the sense that Mills was an ordinary guy who got swept up in a whirlwind, and today finds what happened to him as a young man miraculous enough in its own right that it needs no further embellishment. By contrast, from their teenage years, Peter and Michael have both been compelled to build a mythology around themselves, and, later, around their band. To the point that there’s no anecdote already so good, as it actually happened, that it can’t be improved upon.
Finally, I find the “what does it all matter?” question odd on a forum devoted to R.E.M. The millions of people to whom this minutiae doesn’t matter aren’t on this forum or the R.E.M. Facebook groups debating how “Nightswimming” actually came to be. We are here doing just that, so presumably it matters to everyone reading this thread.