A number of researchers have discussed phase II clinical trials from a Bayesian perspective. A recent article by Tan and Machin focuses on sample size calculations, which they determine by specifying a diffuse prior distribution and then calculating a posterior probability that the true response will exceed a prespecified target. In this article, we extend these sample size calculations to include informative prior distributions using various strategies that allow researchers with both optimistic and pessimistic priors direct involvement in the sample size decision making. We select the informative priors via multiple methods determined by the mean, median or mode of the conjugate prior. These cases can result in varying sample sizes.