Modern medicine has graduated from broad spectrum treatments to targeted therapeutics. New drugs recognize the recently discovered heterogeneity of many diseases previously considered to be fairly homogeneous. These treatments attack specific genetic pathways which are only dysregulated in some smaller subset of patients with the disease. Often this subset is only rudimentarily understood until well into large-scale clinical trials. As such, standard practice has been to enroll a broad range of patients and run post hoc subset analysis to determine those who may particularly benefit. This unnecessarily exposes many patients to hazardous side effects, and may vastly decrease the efficiency of the trial (especially if only a small subset of patients benefit). In this manuscript, we propose a class of adaptive enrichment designs that allow the eligibility criteria of a trial to be adaptively updated during the trial, restricting entry to patients likely to benefit from the new treatment. We show that our designs both preserve the type 1 error, and in a variety of cases provide a substantial increase in power.