Background: Adaptive clinical trials have been increasingly commonly employed to select a potential target population for one trial without conducting trials separately. Such enrichment designs typically consist of two or three stages, where the first stage serves as a screening process for selecting a specific subpopulation. Methods: We propose a Bayesian design for randomized clinical trials with a binary outcome that focuses on restricting the inclusion to a subset of patients who are likely to benefit the most from the treatment during trial accrual. Several Bayesian measures of efficacy and treatment-by-subset interactions were used to dictate the enrichment, either based on Gail and Simon's or Millen's criteria. A simulation study was used to assess the performance of our design. The method is exemplified in a real randomized clinical trial conducted in patients with respiratory failure that failed to show any benefit of high flow oxygen supply compared with standard oxygen. Results: The use of the enrichment rules allowed the detection of the existence of a treatment-by-subset interaction more rapidly compared with Gail and Simon's criteria, with decreasing proportions of enrollment in the whole sample, and the proportions of enrichment lower, in the presence of interaction based on Millen's criteria. In the real dataset, this may have allowed the detection of the potential interest of high flow oxygen in patients with a SOFA neurological score ≥ 1. Conclusion: Enrichment designs that handle the uncertainty in treatment efficacy by focusing on the target population offer a promising balance for trial efficiency and ease of interpretation.