South African universities and other institutions of higher education currently give preference to student applicants from designated "races". This paper argues that such a policy is morally indefensible. Although the imperative to redress injustice is endorsed, this, it is argued, does not entail that applicants may be favoured on the basis of their (purported) "race". Nor can the pursuit of diversity be used to defend racial preference. Next, it is argued that any policy on racial preference must have both a racial taxonomy and a method of assigning individuals to different taxonomic categories. It is argued that both competing methods of categorizing individuals--one subjective and the other objective--are unacceptable. Finally, the paper highlights a number of fallacious responses to criticisms of racial preference. (Contains 2 notes.)