cooper's hawk in captivity, just after a meal

I'd appreciate your suggestions about how to make this or similar

shots more interesting

Coming from an "amateuristic" point of view (cause I am one...), perhaps it might have been better to shoot the whole bird. It would be interesting also to see where the bird was pearched on, Whether on a gloved arm or on a natural tree bark, may tell if the bird is in captivity or in the wilds.

Also, the open skies and almost clear skies behind the bird does not make the latter stand out. Perhaps a little green might help or even if autumn, some red and orange leaves?