Stick with Seasonic, Corsair, Antec for your power supplies. There are a few other good ones out there, but these are probably the top 3.
From what I can see, the Coonix 600W has 2 rails at 18A each. For a total of 36A
To put things in perspective, a Seasonic 460W will produce 38A on a single rail. Many of the Corsair and Antecs can also match or exceed this PSU at 450-500W range.
And thats not even considering effeciency.
The 620W BobKn linked has 48A on a single rail, vs yours that 36A spread over 2.
I would look into putting a good quaility PSU in.
Huge fan of Seasonic myself, but have had both Corsairs and Antecs and they all havbe been excellent. (Most are made by Seasonic anyway) The one linked for example would be a nice upgrade.
--Also, if Im not mistaken, that AMD CPU will pull more power than a i3. Someone please correct me if wrong.
And, FYI, the number on the GPUs box that specifies min. wattage and amps is a generic figure and is intended for the entire system. Not just the GPU.