You can't get rid of the white jaggies when the edges of the image are anti-aliased. When an image is anti-aliased around the edges, you have to use the background color in order to achieve correct anti-aliasing.

If the GIF or JPG specifications allowed for multiple levels of transparency (instead of just on/off transparency), and if all browsers supported that feature, then you could make transparent anti-aliased GIFs and JPGs. But they don't.
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Tony Fabris