post processing - Why does darkening skies in Photoshop cause banding, and how can I avoid it?

I am pretty new to Photoshop (I have Elements 10). When I darken highlights I find that the sky ends up in bands. I have read advice that says to reduce the effect of this by using either blur or noise. However I do not find either of these solutions satisfactory. Blur blurs the edges but I still find the bands obvious and noise looks ugly at the point when it disguises the bands. Is there a better way to darken the sky or remove the bands?

For example: http://www.flickr.com/photos/jamiekitson/8237292309/