In clinical trials designed to evaluate treatment efficacy, it is common practice to terminate a treatment arm in which the observed rate of an adverse event is unacceptably high. This practice may be formalized by a group-sequential test based on a multivariate outcome including both adverse and efficacy events. Recently, Thall and Cheng proposed a family of tests for randomized trials of an experimental treatment versus a standard where patient outcome is bivariate with entries characterizing efficacy and safety. The test is motivated by the idea that clinically meaningful improvements over the standard may be characterized by a two-dimensional parameter quantifying trade-offs between efficacy and safety. We provide optimal two-stage designs based on this test that minimize either the mean sample size under the null hypothesis of no treatment difference, or the maximum sample size if the trial continues to a second stage. A more general group-sequential version of the design also is described, an illustration is provided, and application to the special case of single-arm phase II trials is discussed.