How to get bearable 2D and 3D performance on AMD Radeon HD 6950?

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http://askubuntu.com – I have had an AMD Radeon HD 6950 (i.e., Cayman series) for a couple years now, and I have tried a lot of combinations of drivers and settings with terrible results. I'm completely at a loss as to how to proceed. The open source driver has much better 2D performance, but it offloads all OpenGL rendering to the CPU. What I've tried so far: All the latest stable Ubuntu releases in the period, plus one Linux Mint release. All the latest stable AMD Catalyst Proprietary Display Drivers, and currently 12.11 beta. The unofficial wiki installation instructions for every Ubuntu version and the semi-o (HowTos)