Bailer developed a method for constructing confidence intervals for areas under the concentration-vs-time curve (AUC's) with only one sample per subject but with multiple subjects sampled at each of several time points post dose. We have modified this method to account for estimation of the variances. How the need to estimate variances affects study design is discussed. An extension of Bailer's method is proposed where variances are modeled as a function of the means, in order to get more precise estimates of variances. The modified and extended methods are applied to a rat toxicokinetic study with only two rats per time point per treatment group.