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Can I make it so only certain friends avatars are displayed in the 'My Friends' box?
Yes. Click on the message centre link at the top of the page located under the deviantART header. Once there the link can be found on the right hand column, the link will either be displayed as 'Manage My Friends' or 'Manage Friends' depending on whether you are under the Messages tab or deviantWATCH tab ; either one is fine. Once there uncheck the deviants check boxes under the friends section for those you do not wish to have displayed. If you remove all check boxes, then the 'My Friends' section on the user page will not be displayed.
Note: You can only display 20 avatars in the 'My Friends' box.