You must be joking to run a 350 watts with a 6950. It can't even run a 5770 and will be struggle even with a 5670 or less.
For a 6950 2gb with an ordinary system, you should have a solid 600-650 watts system (assuming you need no headroom) from Corsair or Seasonic or CM SilentPro M/Real Power 700+.