This paper is concerned with bias-reduction properties of that generalized jackknife which pertains to a single-estimator, single-sample situation. Jackknifing is a technique for reducing bias by exploiting the dependence of the bias on sample size. In practice, this is carried out by reestimating the unknown parameter(s) with only part of the sample and combining the new and original estimates suitably weighted to produce cancellation in their biases. The size of the subsample affects both the bias and variance of the jackknife. While few results are available, “minimal data omission” seems sensible on grounds of variance. This paper shows the same is always true on grounds of bias.