The health and genetic data of deceased people are a particularly important asset in the field of biomedical research. However, in practice, using them is complicated, as the legal framework that should regulate their use has not been fully developed yet. The General Data Protection Regulation (GDPR) is not applicable to such data and the Member States have not been able to agree on an alternative regulation. Recently, normative models have been proposed in an attempt to face this issue. The most wellknown of these is posthumous medical data donation (PMDD). This proposal supports an opt-in donation system of health data for research purposes. In this article, we argue that PMDD is not a useful model for addressing the issue at hand, as it does not consider that some of these data (the genetic data) may be the personal data of the living relatives of the deceased. Furthermore, we find the reasons supporting an opt-in model less convincing than those that vouch for alternative systems. Indeed, we propose a normative framework that is based on the opt-out system for non-personal data combined with the application of the GDPR to the relatives’ personal data.