Is there a common phrase or a better, shorter way to describe this man's body position?
"He was lying on his side, propped up on one/his elbow, hand supporting his head."
Which makes it clear he is not in THIS propped up position:
Thanks all for your efforts, but still not quite there. What I'm looking for is a short common phrase that instantly lets you imagine his position in your head, if you are reading it in a book. It's a common enough position. Sitting for a long time on a sofa watching TV or sitting on a bed talking to someone for hours, you may slip down into this position (the guy in my top photo) because it's more relaxed. Or for what I need it for, two people in bed, one asleep dreaming, the other awake, on his side, head propped up, watching the one dreaming. The other position, in the photo above and most of yours posted here, are not in that relaxed manner.