Audit studies testing for discrimination have been criticized because applicants from different groups may not appear identical to employers. Correspondence studies address this criticism by using fictitious paper applicants whose qualifications can be made identical across groups. However, Heckman and Siegelman (1993) show that group differences in the variance of unobservable determinants of productivity can still generate spurious evidence of discrimination in either direction. This paper shows how to recover an unbiased estimate of discrimination when the correspondence study includes variation in applicant characteristics that affect hiring. The method is applied to actual data and assessed using Monte Carlo methods.