Margot,
The first thing that strikes me when looking at the images is that they are dark, very dark. This fact in itself can lead to a degree of posterization.....
I took one of the images (
the second one, of course 
) and opened up the histogram.
In the blue channel 90% of the values are under 64. So what? Well, you are using only 64 different values instead of 256 (for 8-bit work). If you now lighten the photo to full range luminosity, those 64 different values will be occupying a range of 256,
but now they will be spaced out 4 by 4. Which is exactly what posterization is!
Why are they so dark?
Rô