The 2006 'Consensus statement on management of intersex disorders' recommended moving to a new classification of intersex variations, framed in terms of 'disorders of sex development' or DSD. Part of the rationale for this change was to move away from associations with gender, and to increase clarity by grounding the classification system in genetics. While the medical community has largely accepted the move, some individuals from intersex activist communities have condemned it. In addition, people both inside and outside the medical community have disagreed about what should be covered by the classification system, in particular whether sex chromosome variations and the related diagnoses of Turner and Klinefelter's syndromes should be included. This article explores initial descriptions of Turner and Klinefelter's syndromes and their subsequent inclusion in intersex classifications, which were increasingly grounded in scientific understandings of sex chromosomes that emerged in the 1950s. The article questions the current drive to stabilize and 'sort out' intersex classifications through a grounding in genetics. Alternative social and historical definitions of intersex -such as those proposed by the intersex activists -have the potential to do more justice to the lived experience of those affected by such classifications and their consequences.