More recordings like "The Trinity Sessions"?


Apparently the group just set up and began to play and record. Are there more examples other than concerts that were made this way? I'm aware that at one time that was the way it was done but am asking about more recent recordings.
Examples?
Thanks
Steve
scoly1
A very different kind of music but "A Meeting By The River" by Ry Cooder and Vishwa Mohan Bhatt was recorded an hour after the two first met and reportedly was almost completely improvised. A remarkable recording.
Elvis Costello's album My Aim is True was recorded for around 38,000 dollars and the rumour is the first take was what was pressed to vinyl.
Maybe Pat Metheny's One Quiet Night? (I love this thread, btw. Inspiring me to spend $ on more great music.)