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Trade unions are frequently criticised for excluding women from skilled crafts by denying them training. This article examines this argument by estimating the retention and attrition probabilities of men and women in the joint union-management and the unilateral employer-sponsored apprenticeship programs. While men, on average, have higher retention and lower attrition rates than women, joint sponsorship raises women's graduation probability above (and lowers their quit probability below) those of men or women apprentices in unilateral programs.