The Qosand Qm are two leading estimators of the probability of misclassification which are based on the asymptotic expansion of the the expected value of the Error Rate, Pi. The estimators are, however, not suitable for estimating the Error rates for certain ranges of the parameters p , n1, n2and ß.We investigate the regions in which they produce unacceptable estimates , and show that the Qosis, in general, better than the Qmin producing acceptable estimates