Nutritional claims have become a major instrument for providing consumers with information at the point of purchase, enabling them to make nutritionally appropriate choices. This paper deals with two public policy issues linked to the implementation of nutritional claims, i.e. efficiency and equity, in terms of nutritional outcomes and in terms of population targeting. We consider the French breakfast foods market at the household level using 2004 TNS Worldpanel data. We estimate a demand system taking into account the selection issue. For this we use the Shonkwiler and Yen’s procedure which, unlike Heckman’s, allows participation on every market of products to be controlled for. We propose a modification of this approach to address the methodological issue of satisfying the additivity constraint. This procedure is estimated on a set of dairy and cereal-based products which have different health attributes. Our results show that products with health claims play the role they are expected for. The light variants of dairy foods considered here appear to target households with members at health risk, obese or overweight. But interactions between products suggest some limits to efficiency on nutritional grounds. A higher probability of purchasing light products and with higher quantities coincides with higher purchases of biscuits and dairy desserts. Moreover, since lower income discourage the use of products with health claims, equity is not obtained and this should be stressed for policy implications.