Following a post on Hackaday, I dug out an old LCD display and wrote a little program to run it. In normal/active mode, according to my mediocre meter, the whole thing draws 90-100uA. When you put it in sleep mode, it draws nothing. (Edit: I measured with a 5K sense resistor...at 3V, it appears to draw about 3.25uA. Not very much at all!) I hope I can find one of those little SO-8 solar cells to try with this!