Ten more tunes. These are some standards that have kind of a serious aura, that are reasonably-to-very likely to get called. They're not necessarily very hard, but they demand to be approached with respect. It's a subjective thing. Several have unusual forms; I don't feel like any of them just play themselves. Maybe this category only has meaning to me, I don't know.
All or Nothing at All
Central Park West
I'll Remember April
The Night Has a Thousand Eyes
Old Devil Moon
Upper Manhattan Medical Group
For example: I'll Remember April is a commonplace tune with a deeper vibe happening. Alone Together has an odd form. There are several trio recordings of Joe Henderson playing long versions of Invitation that are very hardcore. Strayhorn ballads are very deep and always demand special treatment.
These tunes are most likely to come up with better players. I'll Remember April and Alone Together are the ones you'll mostly likely encounter first. The Night Has a Thousand Eyes also seems to be real popular these days.