Privacy includes the right of individuals and organisations to determine for themselves when, how and to what extent information about them is communicated to others. The growing need of managing large amounts of both clinical and genetic data raises important legal and ethical challenges. This paper introduces some of the privacy-protection problems related to classical and genomic medicine, and highlights the relevance of trusted third parties and of privacy-enhancing techniques (PETs) in the context of data collection, e.g., for research. Practical approaches based on two pseudonymisation models, for both batch data collection and interactive data storage, are presented. The actual application of the described techniques today proves the possible benefits for medicine that innovative privacy-enhancing techniques can provide. Technical PET solutions can unlock valuable data sources, otherwise not available.