I followed the wikilink you supplied and landed at the homepage of the 80 plus certification where I found a datasheet of the 350 W PSU that popped.
Glad I could be of some assistance.
A Bronze-rated PSU at 50% load achieves 85% efficiency, which is about the same as a Silver or Gold at or near 100% load. The difference is, the Bronze costs less and will probably last longer if ran conservatively. Mining places a
continuous load (as in "24/7") on the power supply and graphics cards, which is not the same as "average computer use". So having an adequate power supply is a must, and a little overkill is recommended.
Also if you're running at only 50%-70% load, you don't have to worry about whether the PSU is single-rail or multi-rail so much, as you won't be putting stress on it. You don't have to buy a Gold-rated power supply to be efficient. They are nice though.
PSU's are not intended to run at 100% load for hours on end. Get a good one next time; Corsair, Seasonic, Antec are all good brands. Coolermaster, Thermaltake, Rosewill and the like are just asking for trouble in a power hungry setup.
I'd like to add Enermax to that list. I've had one for years and it's rock solid.