You need to raise you black point on the second image.
Try this on your original image (one which is not heavily compounded by jpeg compression. This is one of the ways I use to improve constrast in photoshop (rather quick and dirty). I typically use a mask to filter the effect giving you better control over what it does to the image.
- Duplicate the original image as another layer.
- On the new layer, use a reasonably pushed curve (non linear stretch). You can either avoid clipping or not worry about it. The image will look rather washed out, but don't be alarmed.
- Then will this layer still highlighted, set its layer blend mode to multiply. You should now see a contrast improvement. If the background darkens too much simply change the opacity of the layer (say from 100% to 80% or whatever you like).
This is also a nice way of removing background noise, but be careful of faint nebulosity. This technique does not work well for all objects. You'll need to experiment.