Hi,
I also suspect some of the banding may come from JPEG compression. A common compression scheme will compress the blue channel of an image more than the others, which can mean blues are more prone to showing artifacts like banding. That's a bit tricky for those of us commonly rendering blue skies! Obviously you were also having issues with the TIFF though, which doesn't do any compression.
As Kadri says banding is a common problem in some aspects of images and there's quite a lot of info on the web about how to minimise it.
Regards,
Jo