How to avoid writing Mary Sues

Two useful articles whose advice does not include "don't make your character awesome in any way" and "don't write about female characters period":

From author John Barnes:
http://thebookdoctorslittleblackbag.blogspot.com/2012/09/facing-up-to-goodness-getting-to-good.html (courtesy of chienne_folle)

From TV Tropes, and surprisingly useful:
http://tvtropes.org/pmwiki/pmwiki.php/SoYouWantTo/AvoidWritingAMarySue?from=Main.AvoidWritingAMarySue