This paper contends that commonly used clinical trial designs do not reflect clinical reality as viewed by patients or physicians. Specifically, randomized phase III designs focus on improvements that are more significant statistically than medically and put an emphasis on avoiding a false positive result that is more appropriate for diseases that are curable, in contrast to acute leukemias. The resultant large sample sizes needed for each treatment restrict the trial to one or two new treatments, although historical reality suggests the difficulty in knowing, without clinical data, whether these are the best of several new treatments. The p value-based statistics discourage use of data from previous patients in the trial to inform treatment of subsequent patients, contravening patients' assumptions. Standard phase II trials focus on a single outcome, ignoring the complexity of medical practice, and ignore prognostic heterogeneity. Finally, although patients are more interested in whether a new treatment is better than another, rather than whether it is active, randomization between different treatments does not begin until phase II trials have been completed. This paper proposes alternatives based on the Bayesian statistical approach. The thesis that I will develop here is that commonly used clinical trial designs are unrealistic in the sense that they do not correspond well to patients' views of medical practice and greatly over-simplify such practice. By emphasizing Bayesian rather than p value-based statistics and focusing on acute myeloid leukemia, I hope to familiarize physicians with some of the many new published designs that address these problems.