Classical phase II trial designs assume a patient population with a homogeneous tumor type and yield an estimate of a stochastic probability of tumor response. Clinically, however, oncology is moving towards identifying patients who are likely to respond to therapy using tumor subtyping based upon predictive markers. Such designs are called targeted designs (Simon, 2004). For a given phase I1 trial predictive markers may be defined prospectively (on the basis of previous results) or identified retrospectively on the basis of analysis of responding and non-responding tumors. For the prospective case we propose two Phase I1 targeted designs in which a) the trial is powered to detect the presence of responding subtype(s) as identified either prospectively or retrospectively by predictive markers or b) the trial is powered to achieve a desired precision in the smallest subtype. Relevant parameters in such a design include the prevalence of the smallest subtype of interest, the hypothesized response rate within that subtype, the expected total response rate, and the targeted probabilities of type I and II errors (α and β). (The expected total response rate is needed for design a) but not for b)). Extensions of this design to simultaneous or sequential multiple subtyping and imperfect assays for predictive markers will also be considered. The Phase II targeted design could be formulated as a single stage or Simon two-stage design. For multiple subtyping corrections to the significance level will be considered. Sample size calculations for different scenarios will be presented. An implication of this approach is that Phase II trials based upon classical designs are too small. On the other hand, trials involving "reasonable" numbers of patients must target relatively high threshold response rates within tumor subtypes. For the retrospective case we will provide the power to detect desired rates in the subtypes and provide the sample sizes required to achieve desired power. Retrospective analysis has the advantages that the analysis can be "supervised" by grouping responding and non-responding tumors; and multiple hypotheses, including hypotheses not formulated at the time of trial design, can be tested.