The bootstrap is a popular and useful tool for estimating the asymptotic variance of complicated estimators. Ironically, the fact that the estimators are complicated can make the standard bootstrap computationally burdensome because it requires repeated recalculation of the estimator. In this paper, we propose a method that is specific to extremum estimators based on U-statistics. The contribution here is that rather than repeated recalculation of the U-statistic-based estimator, we can recalculate a related estimator based on single sums. A simulation study suggests that the approach leads to a good approximation to the standard bootstrap and that if this is the goal, then our approach is superior to numerical derivative methods.