The problem considered is the computation reduction for general delete-djackknife variance estimators. The delete-djackknife estimator was proved consistent (Shao and Wu 1986), and in this article its mean squared error is shown to have ordero(n–2), wherenis the sample size. These properties are not shared by the traditional delete-1 jackknife in some situations. Use of the delete-djackknife, however, requires (nd) recomputations of a point estimate θ, which increases rapidly asnanddincrease. Using techniques from survey sampling, a shortcut can be taken with θ evaluated onlymtimes,m≪ (nd). The efficiency and consistency of the resulting jackknife-sampling (hybrid) variance estimators (JSVE's) are studied. Ifmis chosen so thatn/m→ 0, the increase in mean squared error by using the JSVE is relatively negligible. For the consistency of JSVE,m→ ∞ is sufficient. Hence the JSVE withm<ncan also be used to alleviate the computational burden for the delete-1 jackknife in the case wherenis large and evaluating θ needs large computations. The performance of JSVE is also studied in a simulation study.