Two bootstrapping or resampling strategies were investigated to determine their applicability to estimating standard errors and ensuing confidence intervals on variance components in two-factor random analysis of variance models. In light of prior negative findings regarding the application of bootstrapping to this particular problem, a recommendation of an "optimal" approach to resampling was sought. The study used Monte Carlo simulations to test the variance component estimation accuracy under simultaneous resampling of all effect factors in a random model versus resampling a single factor. Results indicate that single-factor was a preferable method of resampling and produced reasonable estimates of both standard errors and confidence intervals (parametric and non-parametric). Suggestions for the appropriate application of the technique to educational measurement are discussed. (Author/TJH)