I'd like to say that I had a few problems fitting the H60 bracket on my HD6970 because it would sit atop a few components near the GPU, the ones marked in red:

I had to remove the corresponding screw support, so it's mounted with only 3. Still keeps my temps lower than the original cooler (with the H60 it stops at 50C and stays there no matter what I do).
I just hope there is a better way to circumvent this. I still got another bracket left, but I don't want to mod it since I lack the skills for making any precision work.
Maybe I should switch to an H70, since the bracket sits higher. I went for the H60 because it's cheaper and I like the "black square with tubes on the side" look better. (and also because I can change to an H100 in the future).