A new approach is presented for determining the appropriate sample sizes for a series of screening trials to identify promising new therapeutic agents. The formulation of the problem is motivated by recognition of the fact that screening of new agents is a continuing process. Consequently, it does not seem ideal to fix the overall total sample size, as previous authors have done. Instead we fix the error rates and optimize the individual sample sizes to minimize the time to identify a promising agent, using an empirical Bayes formulation. When applied to data from the large historical experience of exploratory vaccination trials at Memorial Sloan-Kettering Cancer Center, the method demonstrates that relatively small individual screening trials are optimal in this setting. The reliability of the results is evaluated using bootstrapping techniques.