A class of delete-d jackknife estimators of the asymptotic variances of point estimators are shown to be consistent when d, the number of observations removed from the original sample, is a fraction of n and the point estimators are generated from a sta¬tistical functional which possesses a weak differentiability property. The computation of the delete-∧ jackknife estimators is almost as easy as the traditional delete-1 jackknife estimator. The results are applied to problems in robust M-estimation