I've greate a gif logo using Fireworks MX. It looks fine on a white background, but when it's over a colored background...there is white along the edges of the text as well as the images in the logo. I've tried to change any white in the logo to transparent, but I'm not getting all of it. It makes it better by maybe 50%, but not completely gone. Apparently, feathering is supposed to work. I've tried a feathering setting of 10 to 200 and nothing works.
The colored background idea is probably best. The "feathering" along type and other object edges is called anti-aliasing and is to help retain the object shape and crispness at various sizes.
When you try to make a background transparent, a few edge pixels in the aliasing are always going to "stick," leaving you with that sparkly white at the edges. So you have to eliminate these pixels completely, which will make your type look choppy and bitmapped, or put the image on the same-colored background before making it transparent, which will effectively hide the anti-alias.
Or, you could try to not design such problems into it by creating objects that will knock out cleanly. :-)