We propose a new design for phase II oncology clinical trials based on two considerations. (1): Currently most phase II oncology trials use complete remission (CR) as the primary end point. The drugs having higher CR rates enter into subsequent phase III trials, which are usually required to demonstrate benefit on survival. Although achieving CR is necessary for prolonging survival, it is not sufficient because patients may relapse shortly after achieving CR. This discrepancy was one of the major reasons for the high failure rates of phase III trials. So it is desirable to evaluate survival outcomes in phase II trials. (2): Assigning more patients to the better treatment arms is more ethical than equal randomization. However, due to the long waiting time to observe the survival outcome, a response-adaptive randomization for survival clinical trials can be inefficient in skewing the randomization probabilities to favor better-performing treatment arms. A natural idea is to use the short-term response information to “speed-up” the response-adaptiveness of the randomization procedure of survival clinical trials? Based on these considerations, we propose a new phase II design that use information on both CR and survival. Their relationship is specified by a Bayesian model. This model is first constructed by using prior clinical information, and then updated continuously by the information accumulated in the ongoing trial. Comparing with a trial using only information on survival, the new design uses fewer patients and takes less time, and can more effectively assign patients to the better treatment arms. Comparing with a trial using only the information on CR, the new design is more reliable in the sense that it picks drug candidates that are more likely to succeed in subsequent phase III trials. Published in Statistics in Medicine. 28(12): 1680-1689, 2009. Free software available on https://biostatistics.mdanderson.org/SoftwareDownload/Default.aspx