As I get more familiar with the music, I start to hear elements in the recorded improvisations that I like, and want to keep, and try to duplicate in subsequent improvisations through the song. Now it's getting harder. I have to remember what I did before and try to do it again just as well as I already know I can. This becomes more difficult as I find new things I want to keep.
Plus, of course, some of the things I like and want to keep are technically difficult things for me at that time that fit well with the song. So not only am I having to remember what to do, those things to do are the challenging things.
After a while, there's enough good stuff in there that the unprepared stuff is starting to sound bad by comparison. But, there are less of those areas than there had been--it used to be the whole song. Those are the areas of freedom in the song. Those are the areas where you can try new things and do new improvisations--and maybe find even more "good things" to keep, further narrowing the regions of freedom, and making them even more precious... as "rigor relief" if nothing else!
Taken to its logical extreme, this process would seem to eventually yield a song with nothing but good stuff in it--though I'm not sure that eliminating all free space is necessarily a good thing. After all, there may be "good things" lurking there that are better than what I used to think were good things.
However, it's not that easy. Now I can make mistakes. I can miss one of those elements that I like and want to keep--make an execution mistake on it. Musical mistakes are always possible too. But it's a lot easier not to make musical mistakes if you're not challenging the limits of your technical ability. Of course, challenging the limits of my technical ability is one of the fun things I like to do, which means that mistakes are inevitable, both musical ones and technical ones.
Now it's hard to know when to stop. When is enough polishing enough?
Probably never.
This, I believe, relates to the self doubt and lack of appreciation of their own material that happens to artists. The desire for perfection.
I try to imagine that for a top professional performing artist, who not only has to be able to do a song perfectly, s/he has to do it consistently and frequently. Of course, practice makes perfect, and the song gets easier and easier and more ingrained in the player's arsenal.
Perhaps a challenge at that point is in not relying on things that have become so easy as to get routine and, hopefully not, boring--to go back to pure improvisation and try to build something new again. Or, analogously, to go find a new piece of music to learn.
Because something that gets set, full to the brim of good things, is probably a composition.
Thus the idea of a "Composed Improvisation": it is still improvisation, but some the elements have been composed and are repeated each time.
Teaching improvisation is a difficult task. However, this process
may provide a mechanism for helping teach, and also for helping practice
it, as well as potentially also being useful for improving a student's
technical development while keeping the technical elements relevant to
the music.