Allied PSUs are, by and large, abysmal. Here's a pretty typical Allied PSU review:
http://www.jonnyguru.com/modules.php?name=NDReviews&op=Story&reid=65
Any time you have to add the negative voltages to get to the specified maximum voltage, stay away.
Any time the 5v rail has more amps than the 12v rail, it's an ancient unit and should be avoided.
Any time you can't find real reviews (that is, using a real load (not PC parts) and a real oscilloscope), stay away.
I expect that unit to go BANG when faced with a higher draw GPU. Actually I'm kind of surprised it hasn't died or killed something already, as the caps are most likely Asia-X / Fuhjyyu, which have a limited lifespan at best.
In short, it's new PSU time.
That PSU only meets the specs
if you believe the label, which is almost certainly false information. Given that the label is about as useful in figuring out the quality as the national flag flown by a pirate ship is in figuring out whether it's a pirate ship, you can't judge the PSU based on said label at all. Other, of course, than by the name stamped on it. In this case that is "Allied", which translates to "run away!"
My advice: Do not turn that PSU on at all, let alone with parts you don't want to fry.