This question came up by some members and i decided to make a tutorial, i hope this helps.
(thread will be moved to a more appropriate place once the forum was updated
after creating your avatar, instead of going to "file - Save as", you go to "file - save for web & device", as shown in the thumbnail below.
you will see 4 pictures with 4 different resolutions. you take the picture at front row, at right. you click on it, until it is selected. a blue square is put all around it, like in the thumbnail below.
Now, you reduce the quality, until it drops under 15kb. depending on how the picture is, how many different colours, or details you will have to reduce until 80quality or sometimes 95 quality will do it too. In my thumbnail you will see, 81 quality was required and the quality of the picture isn't reduced in my eyes. it's still a beautiful picture. hehe, see thumbnail below.
once you are under 15kb, click on "save" and you have a avatar below 15kb
i hope this helps a bit