Enteric fermentation from dairy cows is a major source of methane. Significantly and rapidly reducing those emissions would be a powerful lever to mitigate climate change. For a given productivity level, introducing fodder with high sources of n-3 content, such as grass or linseed, in the feed ration of dairy cows both improves the milk nutritional profile and reduces enteric methane emissions per liter. Changing cows' diet may represent additional costs for dairy farmers and calls for the implementation of payments for environmental services to support the transition. This paper analyzes 2 design elements influencing the effectiveness of a payment conditioned toward the reduction of enteric methane emissions: (1) the choice of emission indicator capturing the effect of farmers' practices, and (2) the payment amount relative to the additional milk production costs incurred. Using representative farm level economic data from the French farm accountancy data network, we compare enteric methane emissions per liter of milk calculated with an Intergovernmental Panel on Climate Change Tier 2 method, to baseline emissions from a Tier 3 method accounting for diet effects. We also quantify the additional milk production costs of integrating more grass in the fodder systems by estimating variable cost functions for different dairy systems in France. Our results show the relevance of using an emission indicator sensitive to diet effects, and that the significance and direction of the additional costs for producing milk with a diet containing more grass differ according to the production basin and the current share of grasslands in the fodder crop rotation. We emphasize the importance of developing payments for environmental services with well-defined environmental indicators accounting for the technical problems addressed, and the need to better characterize heterogeneous funding requirements for supporting a largescale adoption of more environment-friendly practices by farmers.