Conventional randomized clinical trials provide a powerful and scientifically rigorous method for comparing medical therapies, but designs using 50-50 randomization (or any other constant assignment probabilities) can raise ethical difficulties when there is strong evidence, either a priori or from study data, that one of the therapies may offer great benefit to individual patients. This article describes such a situation, the evaluation of extracorporeal membrane oxygenation (ECMO) for treatment of persistent pulmonary hypertension of the newborn (PPHN). For many years, the mortality rate among infants with severe PPHN treated with conventional medical therapy (CMT) was 80${\tt\%}$ or higher. ECMO treatment of PPHN was introduced in 1977 and, by 1985, several centers had reported survival rates of 80${\tt\%}$ or better in infants treated with ECMO. Only one randomized trial was reported by the end of 1985. This trial used a randomized play-the-winner design. Eleven patients received ECMO therapy and all survived. Only one patient received CMT and this patient died. In part because of the success of ECMO therapy, this trial provided very little comparative data on the two therapies. The author and medical colleagues reviewed these data in 1985 and concluded that they did not justify routine use of ECMO without further study. A review of historical experience at two Harvard hospitals showed, however, that 13 infants had developed severe PPHN in 1982 and 1983 and 11 (85${\tt\%}$) had died. All received CMT. Thus, there was a strong possibility that a randomized trial would show large differences in survival rates in the ECMO and CMT groups. To balance ethical and scientific concerns, we designed a clinical trial with a treatment assignment procedure that would begin as conventional randomization but switch to a single therapy study when a prespecified number of deaths was observed in either group. This article describes the study design and results. Nineteen (19) patients were enrolled during the randomized phase; 6 of 10 survived in the CMT group and 9 of 9 in the ECMO group. In the second nonrandomized phase, 20 patients were assigned to ECMO therapy and 19 survived. The survival rates in the two treatment groups were significantly different $(P < .05$ with curtailed sampling) and the profile likelihood for the difference in survival rates between the ECMO and CMT groups gave a one-sided 95${\tt\%}$ confidence interval with a lower limit of .131. We conclude that ECMO therapy increases survival relative to CMT therapy in patients with severe PPHN.