Biomarkers are critical to targeted therapies, as they may identify patients more likely to benefit from a treatment. Several prospective designs for biomarker-directed therapy have been previously proposed, differing primarily in the study population, randomization scheme, or both. Recognizing the need for randomization, yet acknowledging the possibility of promising but inconclusive results after a stage I cohort of randomized patients, we propose a 2-stage phase II design on marker-positive patients that allows for direct assignment in a stage II cohort. In stage I, marker-positive patients are equally randomized to receive experimental treatment or control. Stage II has the option to adopt "direct assignment" whereby all patients receive experimental treatment. Through simulation, we studied the power and type I error rate of our design compared with a balanced randomized two-stage design, and conducted sensitivity analyses to study the effect of timing of stage I analysis, population shift effects, and unbalanced randomization. Our proposed design has minimal loss in power (<1.8%) and increased type I error rate (<2.1%) compared with a balanced randomized design. The maximum increase in type I error rate in the presence of a population shift was between 3.1% and 5%, and the loss in power across possible timings of stage I analysis was less than 1.2%. Our proposed design has desirable statistical properties with potential appeal in practice. The direct assignment option, if adopted, provides for an "extended confirmation phase" as an alternative to stopping the trial early for evidence of efficacy in stage I.