Organ transplants are not regarded as an exclusively medical process, because they involve financial, religious, philosophic, and bioethical parameters. It becomes clear that if they are to achieve their purpose, which we believe extends well beyond the medical dimension, the creation of a comprehensive framework of communication between the involved parties is of paramount importance. The aim of this paper is to present an outline and a number of considerations regarding the communicational, bioethical, and legal issues that arise from a rather dramatic state of affairs in Greece today: In 2012 the rate of organ transplants stood at only 7 per 1 million of the population. The outdated legal framework and the lack of trust on the part of patients and the public have led to a highly inefficient system that is lagging behind in many respects. The proposition made in this paper is that there is a need for a new system of communication between doctors, patients, relatives of patients, and hospitals: bioethical mediation. This is a system that has played a vital role and has produced astounding results in other countries. There is also every indication that the introduction of such a system is crucial for Greece, especially as the symptoms of the acute financial crisis are become fully visible and tangible. Mediation aims to identify solutions that are oriented toward the interests and wishes of patients, are acknowledged and accepted by all parties involved, and are in tune with the values and the principles of medical practice.