Image edit help (remove white background)

Hello,

I have a logo that is in JPG format and has a white background. But I want to use this logo on a skin with a dark background, so I need the white to be removed and replaced with transparency.

I tried it myself using Paint.NET, but here is the failed result (the edges of the letters and characters look very choppy):

View attachment 344

If somebody could make this transparent and save it as a PNG image, I would greatly appreciate it!

White JPG version is attached.
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I have it a shot in CS4 but due to the effects of the lettering it gave pretty much the same result for me as well

 

D: I can try when I finish the other image I am doing.