A technique based on the bootstrap is presented for assessing the simultaneous confidence level of k small-sample confidence intervals for multivariate Bernoulli marginal frequencies. The small-sample intervals used are those of Clopper and Pearson (1934, Biometrika 26, 404-413) and require iterative computation. To estimate the simultaneous confidence level, the multivariate Bernoulli vectors are resampled via the bootstrap and the Clopper-Pearson intervals recomputed on each pseudosample. The bootstrap estimate is then the proportion of times (computed via Monte Carlo) that all the k intervals computed by resampling contain the original sample frequencies. The technique is applied to single-sample HLA data.