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Few studies have focused on the multivariate joint design of drought properties. Using daily streamflow data, this paper analyzes the impacts of pooling and exclusion of drought events in determining hydrological drought properties. The bivariate joint distributions of droughts were determined by using copulas. A novel method for bivariate design, the most-likely weight function, was applied to select design pairs for drought properties. The confidence interval of design curves of a given joint return period was limited by the measure of the joint probability density function due to the uncertainty of the estimated copula parameter. By comparing subseries separated by the low-flow change point, drought properties and their joint distributions, and designs were investigated under changing environment. Results showed that it was appropriate to set the pooling and excluding ratios as 0.2 and 0.41, respectively. The dependences of drought properties were positive and Archimedean copulas fitted well the bivariate joint distribution of droughts. The uncertainty of design duration-peak was remarkably greater than that of duration-severity and severity-peak. The design duration-severity was considerably stationary. Under changing environment, drought duration, severity, and peak remarkably decreased.