In many developing countries, a significant portion of the wage distribution is found below the legal minimum wage. In order to fully understand the nature of this non-compliance, we need to compare the counterfactual wage distribution without the minimum wage law to the current wage distribution. Such a comparison could reveal partial compliance, where employers raise wages some of the way to the minimum wage, to balance out the benefits of non-compliance with the costs and penalties to the extent that they depend on the gap between the legal minimum wage and the wage actually paid. This paper presents a simple model of such partial compliance and uses its predictions to structure an empirical investigation of the impact of introducing a minimum wage law for agricultural workers in South Africa. We find that partial compliance is indeed taking place and further, the lowest wages are being raised disproportionately, consistent with the predictions of the model. JEL codes: J23, J25, J31, J32, J38, J43