Often I want to edit images, e.g. change color, that once had some transparency (like "transparent", see attached) but, by the time I get them, have been saved on a white background. I can save the white as transparent so that I end up with an image like "white_border" (see attached). But when I fill this image with color the off white pixels are filled with the full color and so appear pixelated (see "pixelated").
How can I change the color yet retain the transparency?