For Avatars I use Omega and sometimes Biturn. But the latter can be problematic. Omega is pretty much the standard, but it forces you to load a tex before converting a new bmp, I think it gets all the info for the new tex from the old one you load. I've used biturn to make a custom tex that was unpaletted at 2048x2048, but omega refused to load it and ffvii won't display tex files made by biturn.
kula_wende, you see the white drop shadow. to get ride of it either make the avatar bigger, or use paint.net to crop and resize the pic and save it as a 256 bmp, then copy it, open the original avatar in regular paint and paste it then save and convert with omega. I'm not sure why but when I do it all in Photoshop the tex file that omega makes is moved up and to the left, but with paint the tex file is always in the right place. I have no idea why but it always happens that way.