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Some ins and outs of transparent GIFs and PNGs.
     Before I begin, I suggest you review these FAQs. They will give you an understanding of image file formats that will be greatly helpful, regardless of how well you understand them.

    Here we go. So I'm making a pic. I will make an image I want to post as a transparent gif. In PSP, the transparent area is a checkerboard. You can change the colors of it to anything you want. The doodle is ready. Mitsuko 1/1. Hah hah. She seems nonplussed. The edges of the text is hard, fully aliased. There isn't the least bit of smoothness to them.

     Now I will flatten the layers. (I have my background palette color set to white for this example, and so the transparent areas of the image will become white.)

     That's done. The image is now a single layer, the background layer. Now I will paint in the area I want to be transparent. I use bright green as my transparency color, because I almost never use it in my work. When the colors are reduced to 256, the green will not appear anywhere outside of where I painted it, because it's not even close to the other colors in the image. It will not be used to replace any other colors.

    Setting the color green as the transparent color... Now I will post it on the web. Hey, wtf?! There's crud all around poor Mitsuko-tan! Why?!

     Dig it. Transparent GIFs use 1-bit transparency. This means the pixel is either solid or transparent, nothing in between. The white background that was replaced with the green was fully white, not even light gray with a tolerance in either direction. Only the white was replaced. The white that blended in with the black became gray. The text is fine because it was drawn with a hard-edged brush. No smoothing whatsoever. Fully opaque, so none of the transparent background showed through. The only way to avoid this halo of junk is to trim the border of the area that will be affected, or to make sure everything bordering the transparent area has a hard edge. Sometimes this can look like crap. In the days ofl the ancient internet, this rarely mattered, because most web pages were gray or white. Now we have thousands upon thousands of colors, and background images. One has to carefully construct their transparent images...

...unless they go with translucent PNG... but I'm not even going to explain that today.

     Make sure the portions of your image that border the transparent areas have a hard edge! You don't want shitty ghost halos appearing on your nifty works.