The little clump is the eagle Christina. The big spike is the sky. There will be some eagle in the big spike as well. If the exposure had been correct the eagle aspect of the histogram would be broader. The sky just about uses up all of the dynamic range and the eagle very little. In a back lit shot like that a decent exposure for the eagle is bound to clip the sky as the dynamic range needed to get both is well over what the camera can handle. How much to compensate on the meter readings in this situation depends on the camera.
The dark end, dark subjects and low light are difficult but if it's a situation where there are no highlights to clip or that doesn't matter some degree of over exposure is the best option. The camera histogram can give you a rough idea of the scope for this - use up some of the spare space on the right or decide how much to clip off.
In both cases the idea is to get the subject out of the noise region. In the case of the eagle I don't thin noise would be a problem if the exposure had been corrected. Saying it can't be seen when the eagle shot is reduced to web size doesn't really help as the eagle still wont look right,
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Personally when things are that dark I don't think it's a good idea to just increase the exposure. If you look carefully at the shot I posted you will see some colour artefacts. That's not noise it's what happens when dark areas are lifted up. The point to stop at is prior to when they become obvious.
I don't have a shot such as the one you requested but I do have something from a jpg which is essentially what can be done from raw using an S curve and then processing that. i have just brightened up 2 areas as far as they can go. The shot was taken to get zero clipping in the sky.
Using and insane curve out of curiosity from raw I extracted as much as possible but as you can see the shot is then unusable.
It's all a case of getting the subject in the usable range of the camera.
The final version was like this one which looks to me like I over sharpened a bit.
John
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PS just noticed from the clouds that I have made those from 3 different shots - you'll just have to trust me.
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