If you're running compiz, then of course you have hardware-accelerated 3D. Where did you get the idea you don't?
The "radeonhd" driver is long deprecated. "radeon" handles all GPU's with radeon(hd) in their name.Make sure you have the open-source drivers for -ati and -radeon installed (you may need -radeonhd with your "modern machine").
Code:man radeon
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