In the academic year 2017/18 there is an opportunity for the public Spanish universities to design specific processes of undergraduate admissions. With this aim, we have investigated whether proceeding in this direction helps to promote the quality of universities for their students. Taking as reference the structure of the EFQM model, we have studied the impact on student satisfaction regarding how to determine the admission of students and improving their perception in terms of the reputation and image of the institution. Following the completion of a questionnaire on a sample of 467 students from a private university with proven experience in the specific design of the admissions process, we have obtained evidence that a specific design can promote student satisfaction as well as serve to enhance the perception in terms of reputation and the image of the university students have of it.