Privacy is a major good for users of personalized services such as recommender systems. When applied to the field of health informatics, privacy concerns of users may be amplified, but the possible utility of such services is also high. Despite availability of technologies such as k-anonymity, differential privacy, privacy-aware recommendation, and personalized privacy trade-offs, little research has been conducted on the users' willingness to share health data for usage in such systems. In two conjoint-decision studies (sample size n=521), we investigate importance and utility of privacy-preserving techniques related to sharing of personal health data for k-anonymity and differential privacy. Users were asked to pick a preferred sharing scenario depending on the recipient of the data, the benefit of sharing data, the type of data, and the parameterized privacy. Users disagreed with sharing data for commercial purposes regarding mental illnesses and with high de-anonymization risks but showed little concern when data is used for scientific purposes and is related to physical illnesses. Suggestions for health recommender system development are derived from the findings.