Ko(1998, 1999) proposed certain flexible two-stage plans that could be served as one-step interim analysis in on-going clinical trials. The proposed Plans are optimal simultaneously in both a Bayes and a Neyman-Pearson sense. The Neyman-Pearson interpretation is that average expected sample size is being minimized, subject just to the two overall error rates $alpha$ and $eta$, respectively of first and second kind. The Bayes interpretation is that Bayes risk, involving both sampling cost and wrong decision losses, is being minimized. An example of this correspondence are given by using a binomial setting.