Not a lot of options with the backgrounds on the day I took those kestrel photos, it was a dull and murky sort of day and the only opportunities I had were to shoot them against the grey sky.
Regarding the exposure, I think the one in the tree looks about right to my eyes (assuming you're talking about how bright they are and not shutter speeds which I typically lock around 1/800s). Any darker and the detail around the eyes would disappear into the shadows.
The flying one was very underexposed due to the grey sky and it's a really heavy crop. Again, I've adjusted the exposure so you can see detail around the eyes. I think the main problem with that one is a combination of the original underexposure and bird being very tiny in the frame, so it's really stretching the definition of what might be classed as acceptable image quality as there's not a lot of detail to play with and what there is was mostly crushed into the shadows in the original image, making the recovered details look a bit washed out. The only reason I included it was that I like the pose of the bird and the fact it was looking straight at me.
Here's a comparison of the unedited images compared to the final results.
