I agree with your self critique. The view of the tail is pleasing. I also like the pose and with a nice head angle. The slightly open beak adds interest for me. The perch and background are also nice. Overall a lovely image.
Since you do not seem adversed to removing distractions from your image (you stated you remove a branch) and you stated that your not crazy about the shadow, I took some time attempting to see if I could remove the shadow running through the tail. Although the shadow doesn't bother me that much, I thought it would an interesting comparison. It took longer than I care to admit and I am sure with a little more care and the original file one could do a better job. I almost forgot but I also changed the brown stop above the head to green.
Again a lovely image that I have enjoyed. Thanks for sharing.
Phil - you did an amazing job with that! I guess after looking at it now, it looks a bit unnatural *completey* removed, since my mind knows there should be a shadow there. I think I might try just lightening it a bit so that it is not quite so distracting. Thanks for you fine efforts!
Jim, I tend to agree with you. Making the shadow less strong/harsh as opposed to completely removing it probably is the best option. It was interesting exercise.