The 4770 is borderline as far as needing a power cable anyway. I would say that as long as your PSU has a dedicated PCIE plug, not one you made up from a converter then you are fine.
If the PSU is a Chokemax, it will blow if loaded to 75% of its label (in this case 337.5W). OTOH, a quality PSU like a 380W Antec Earthwatts would have no trouble at all. So, it would indeed help to know the brand and model of your PSU.