In many jurisdictions, courts and the related tort liability rules have failed to adequately address conflicts arising from healthcare delivery that has caused harm. The litigation model – the classic model used to deal with medical liability – must be, if not replaced, at least supplemented by another model, and alternative dispute resolution is best suited to this task. Because conflicts are resolved in a less adversarial environment than a courtroom and led by people with knowledge of both medicine and law, alternative dispute resolution promotes a congenial procedure, is faster and cheaper than traditional litigation and can provide more satisfactory outcomes for all parties. This paper reviews some of the failures of litigation as a means of resolving disputes related to medical liability and considers how alternative dispute resolution methods can address these failures, providing some examples from civil law jurisdictions in Europe.