The increasing potential for commercial applications in biotechnology has given rise to new legal and ethical questions with regard to ownership of human tissue. As the potential value of human cells and tissue has risen, so have donors' calls for a share in the profits. However, in a recent California ruling (John Moore vs the Regents of the University of California), the court once again held to its traditional position that individuals do not hold property rights in their own tissue and cells. We will show that, in the rare case where tissue value may be determined prospectively, a one-time payment (and, hence granting a property right) is efficient. Moore is such a case. In general, however, the transactions costs of granting full property rights to donors of tissue and cells outweigh the benefits of such a change in policy.