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Any suggestions on how to "fill-in" the shade without using a flash

that would blast away the details?

I wouldn't fill in the shade at all, myself, I think it works very nicely as it is. Personally, I'd crop a little off the top to increase the bird's dominance. I'm not sure I like it as I 'know' owls have two eyes but it's certainly different.

It would have been nice to capture more detail in the eye and the edges are a little soft but you probably had to shoot with the lens wide open. Unfortunately in wildlife photography one cannot ask the subject to face the light source. Good shot!