The hiring process is currently the least understood aspect of the employment relationship. It may be the most important for understanding the broad processes of stratification with allocation of demographic groups to jobs and firms. The lack of knowledge is due to the difficulty of assembling data on the processes that occur at the point of hire. Against this background we analyze data on all applicants to positions in one of the largest Scandinavian banks in 1997-1999. The hiring agents in the organization are fully conscious and concerned about the nonconscious biases and gender schemas they carry when making hiring decisions. Their effects on hiring are considered to be beyond dispute: Women are at a clear disadvantage. For actual hiring practices we found that the opposite is true: Women are at an advanatage in getting offers. Two organizational practices may lead to female advantage, with relevance for other countries as well. The hiring agents had been educated about the role of nonconscious biases, which perhaps mitigated their effects. But they had also been instructed to search actively for qualifieed females in the applicant pool. With no qualified females in the first pass, they go through the pool a second and third time hoping to find one. we discuss reasons why the interpretations and meanings the hiring agents attribute to the hiring process are so at odds with what actually occurs.