SUMMARY: This paper is concerned with protocols for sequential clinical trials which meet the classical statistical criteria of significance and power and which tend to assign the majority of patients to the superior method of treatment. The object is to test the null hypothesis that there is no difference in mean survival times associated with two treatments. It is assumed that survival times are exponential with parameters, death rates, which depend upon the treatment and that patients arrive sequentially over a period of time and are assigned immediately to a single treatment. The assignment rules utilize the data collected about patients already treated to choose the treatment for the next patient. The trials are terminated when the likelihood ratio crosses a given boundary. It is shown that the operating characteristic is insensitive to the assignment rule, and that the expected number of patients receiving the inferior treatment can be markedly reduced by the use of data-dependent rules. © 1971 Oxford University Press.