The resubstitution estimator of classification error rates is known to have both an optimistic bias and a large variance. Modifications to this method have addressed these problems. the bootstrap estimator, for example, uses a resampling scheme to reduce bias, and the NS method uses a smoothing algorithm to reduce variance. In this paper we show that the use of a bootstrap adjustment to reduce the bias of the NS method results in an estimator which combines the advantages of small bias with low variance, and is therefore preferable to existing resampling estimators. In addition, a new smoothed estimator with reduced bias is introduced which may eliminate the need for resampling in somesituations.