In design under uncertainty, random distributions are often determined by expensive sampling tests. A key question is whether to invest in more samples or live with a reduced performance by fewer samples due to large uncertainty. The question is particularly difficult to answer when the type of distribution is unknown. This paper investigates the tradeoff between performance and conservativeness in estimating B-basis allowables, using experiments on composite plates with holes. Two approaches that do not require a distribution type are examined: (1) bootstrap confidence intervals and (2) Hanson-Koopmans non-parametric method. Based on the study, it is found that the Hanson-Koopmans method was more conservative than the bootstrap method because the latter penalized allowables for small-size samples. For a small number of samples (less than 29), conservative estimations are preferred over accuracy to account for the large uncertainty. Based on this observation, the bootstrap-assisted Hanson-Koopmans method is proposed to enhance the conservativeness. For the tested cases, the performance penalty using the bootstrap-assisted Hanson-Koopmans method for a small number of samples is found to be substantial.