We propose a design strategy for single-arm clinical trials in which the goals are to find a dose of an experimental treatment satisfying both safety and efficacy requirements, treat a sufficiently large number of patients to estimate the rates of these events at the selected dose with a given reliability, and stop the trial early if it is likely that no dose is both safe and efficacious. Patient outcome is characterized by a trinary ordinal variable accounting for both efficacy and toxicity. Like Thall, Simon, and Estey (1995, Statistics in Medicine 14, 357-379), we use Bayesian criteria to generate decision rules while relying on frequentist criteria obtained via simulation to determine a design parameterization with good operating characteristics. The strategy is illustrated by application to a bone marrow transplantation trial for hematologic malignancies and a trial of a biologic agent for malignant melanoma.