Was bisexuality a widespread feature of ancient Greek society? This question is an instance of cross-cultural projection -- of taking the means through which people are categorized in one culture and applying it to members of another. It’s widely held by those who think that sexual orientation is socially constructed that its projection poses a problem. In this paper, I offer a more careful analysis of this alleged problem. To analyze projection, I adapt Iris Einheuser’s substratum-carving model of conventionalism to (...) fit the specific needs of social construction. Using this model, I show that projection is conceptually coherent, and so does not for that reason pose any problem. Along the way, I identify some of the epistemic difficulties facing projection. While these difficulties are formidable, they are not substantially affected by the constructivist claim. I therefore conclude that there is no unique problem facing the projection of a socially constructed sexual orientation. (shrink)