The public-health community views the mandatory labelling and taxation of fat as promising tools to control the growth of food-related chronic disease. This paper is the first to propose an ex ante evaluation of these two policy options in an oligopolistic setting with differentiated products and heterogeneous demand. Using household scanner data on fromages blancs and dessert yogurts, we separately identify consumer preferences for fat and front-of-pack fat labels by exploiting an exogenous difference in legal labelling requirements between these two product categories. Demand estimates are then combined with a supply model to evaluate both policies. In the absence of any producer price response, making fat labels mandatory reduces the fat supplied to regular consumers in this market by 38%; an ad-valorem tax of 10% (5%) on the producer price of full-fat (half-skimmed) products has a similar impact. Allowing producer price reactions, however, yields much smaller effects: a 9% drop for the fat tax, and a fall of only 1:5% for mandatory labels. Producers thus neutralise up to 96% of the impact of mandatory labelling on demand, via large price cuts on products with large ex ante margins. This illustrates how market forces are largely able to defeat the intended effect of market-based public-health interventions.