As an example, “Banshee Legs Bell Hassle” is an improvisation by King Crimson’s three current drummers, but I can’t really see anything better than song for it.
Whether an improvisation counts as a work at all is interesting. If it does, but it doesn’t seem to fit song, just remember that it’s ok for something to not have a type
I argued for reproducibility as a guide whether to create a Work.
Personally, I’d take the lazy option and skip creating the Work until someone claims that another recording is of the „same“ piece. If nobody ever does that, there’s no need for a Work either.
Well, the piece I linked is currently on two official KC releases: “Live in Toronto”, and “Radical Action to Unseat the Hold of Monkey Mind” - which was recorded live in Japan. Both releases have writing credits for the band members performing them.
KC are also known for taking improvs they’ve done in the past, stripping the audience sound, and sometimes adding more in the studio. “Trio”, from “Starless & Bible Black, is one example (which is also notable for having a writing credit for Bill Bruford when he sat out the entire improv because he didn’t think he could make it any better than it was with his drumming) of four on that album.