Bigenderism maintains there are only two genders, which correspond with the two sexes, male and female. Basic bigenderism requires that legal documents and public institutions designate a single invariant gender (that is, sex). Strict bigenderism applies these categories in a social context that stigmatizes "imperfect" men and women who do not reach ideals set by the bigenderist schema. I discuss these concepts and their implications, present three models that successively weaken bigenderist assumptions, and argue for the most radical of the (...) three. (shrink)