Agree bill and eye look a bit too saturated.
Ideally, would like head to be parallel or angled toward viewer rather than angled away.
Pose makes for a tricky composition IMO.
Might go a bit more toward vertical, i.e. not as wide.
I like the overall pose especially the wings. I agree the saturation is a bit much, and comp-wise I would prefer more room above than below. A bit of noise on the near wing's darker area...did you need to lighten in post? (exif info would help...)
A beautiful capture. The signature detracts from the simplicity of the image. I like Mike's comment about a little off the width to make it more vertical.