South Africa has 23 universities, of which five are placed in one or more of the 2011 Shanghai Jiao Tong, Times Higher Education, and Quacquarelli Symonds world university rankings. The five are: Cape Town, Witwatersrand, KwaZulu-Natal, Stellenbosch and Pretoria. They are ranked above the other 18 universities, with Cape Town in top position, mainly because they have significantly higher publication and citation counts. In the Shanghai Jiao Tong ranking Cape Town's Nobel Prize alumni and highly-cited researchers give it an additional lead over second-placed Witwatersrand, which has Nobel Prize alumni but no highly-cited researchers. KwaZulu-Natal, in third place, has no Nobel Prize alumni but one highly-cited researcher, which places it ahead of Stellenbosch and Pretoria despite the latter two having higher publication output. However, in the Times Higher Education ranking, which places Cape Town first and Witwatersrand second, Stellenbosch is ranked but not KwaZulu-Natal, presumably because the publication and citation counts of Stellenbosch are higher. The other 18 universities are ranked by the SCImago and Webometrics rankings in an order consistent with bibliometric indicators, and consistent with approximate simulations of the Shanghai Jiao Tong and Times Higher Education methods. If a South African university aspires to rise in the rankings, it needs to increase publications, citations, staff-student ratio, and proportions of postgraduate students, international students and international staff.