The increased prevalence of lifestyle-related illnesses particularly in western countries calls for public action. A poor diet is a key explanatory factor to this development. Previous research has addressed the problem of unhealthy food consumption behavior by looking at how taxes may function as an instrument to change purchase behavior from less healthy products to healthier ones. In this paper we address this issue by looking at the effects of discounts depending on whether healthy or less healthy products are available at a discount. Our study is based on weekly purchase data from a Danish household panel for the period 2010-2011. Interestingly, from a public health perspective our findings suggest that there is an asymmetric effect of discounts depending on the fat content of the product. Furthermore, our results point at two classes of consumers where the asymmetric effects go in different directions.