In 2015, the South African Government, organised business and organised labour agreed to the introduction of a national minimum wage (NMW) in principle, but without any agreement over the level at which it should be set. One of the key arguments for a high NMW is that the experiences of other countries (including especially Brazil and Germany) supposedly show that a NMW can be increased rapidly to a high level and covering a majority of the workforce without any adverse effects on either economic growth or employment. We show that this is a misinterpretation of comparative experiences because in both advanced capitalist and middle-income economies NMWs are set at modest levels, covering the minority of lowest-paid workers, and taking into account the real risks of job destruction. Most countries have slowly raised minima because low unemployment made them confident that modest increases would lead to little or no job destruction. South Africa’s current sectoral minima are already broadly in line with minima in most other countries. International experience does not support the contention that South Africa, with its exceptionally high unemployment rate, should raise rapidly the NMW to a very high level without regard for job destruction.