In addition to the aim of mapping and sequencing one human's genome, the Human Genome Project also intends to characterise the genetic diversity of the world's peoples. The Human Genome Diversity Project raises political, economic and ethical issues. These intersect clearly when the genomes under study are those of indigenous peoples who are already subject to serious economic, legal and/or social disadvantage and discrimination. The fact that some individuals associated with the project have made dismissive comments about indigenous peoples has confused rather than illuminated the deeper issues involved, as well as causing much antagonism among indigenous peoples. There are more serious ethical issues raised by the project for all geneticists, including those who are sympathetic to the problems of indigenous peoples. With particular attention to the history and attitudes of Australian indigenous peoples, we argue that the Human Genome Diversity Project can only proceed if those who further its objectives simultaneously: respect the cultural beliefs of indigenous peoples; publicly support the efforts of indigenous peoples to achieve respect and equality; express respect by a rigorous understanding of the meaning of equitable negotiation of consent, and ensure that both immediate and long term economic benefits from the research flow back to the groups taking part.