The article argues that altruistic giving based on anonymity, which is expected to promote social solidarity and block trade in human body parts, is conceptually defective and practically unproductive. It needs to be replaced by a more adequate notion which responds to the human practices of giving and receiving. The argument starts with identification of the main characteristics of the anonymous altruistic donation: social separation of the organ donor (or donor family) from the recipient, their mutual replaceability, non-obligatoriness of donation, and non-obligatoriness of reciprocation on the recipient's part. Since these characteristics are also central to typical market relations, anonymous altruistic donation not only cannot promote solidarity but may encourage proposals for (regulated) markets of transplantable organs. Thus, transplant ethics needs to be reframed. It needs to be rooted in, rather than promote, the practices of giving and receiving known to human societies. As the basis for such reframing, the idea of sharing in another's misfortune is proposed. It relies on the human practices of giving and receiving and, with appropriate regulatory safeguards, can provide a better conceptual basis for blocking commercial exchanges of human body parts.