LiDAR inventories were carried out to estimate the mean volume and variance in Eucalyptus globulus and Eucalyptus nitens stands. Uncertainty of the population estimates was examined using approximations based on the bootstrap method. Three methods were tested, the traditional bootstrapping-pair method (Method 1) and two additional methods in which the residual variance of the models was incorporated. Method 2 incorporated the residual variance in homoscedastic structure and Method 3 incorporated the heteroscedastic residual variance. Bootstrapping-pairs based on Method 3 generated similar estimates for the mean volume and slightly higher estimates for the variance as the traditional method (Method 1). Variance estimates obtained with the traditional bootstrapping-pairs method could be biased due to the presence of heteroscedasticity. Method 3 was found to best estimate the variance of the mean volume in LiDAR inventories, when the models that describe the relationship between stand variables and LiDAR metrics do not meet the assumption of homoscedasticity. It is shown that the uncertainty of the estimation of the average volume decreased in stands with a larger area, stabilizing the uncertainty of estimates in stands with areas larger than 50 hectares. Our results suggest that the residual variance in the heteroscedastic structure must be incorporated to avoid bias when bootstrapping-pairs are used in small area stands (less than 5 hectares).