Thanks again for all the comments.
Russ, I think you're right that cropping shouldn't be the first thought and that shots shouldn't generally be taken with cropping in mind. That said, I did think the advice to crop and try it was valuable, and by choosing a square format (rather than a "perfect" crop to suit), it made me think about the composition further (do I give the bird space to fly into, make it central, how about the framing of the branches, and so on).
Back to the original, though, and I do like the extra branches which make me think of birds' nests and the skeleton of the bird that can be seen. So good advice for me to look at removing the distraction without cropping.
I'll play with that over the weekend.
I don't often post up here, but the comments always provide insights and food for thought, which is the point :-)