In the present study we estimated the genetic parameters of enteric methane emissions (EME) traits predicted from milk fatty acid profile (FA) and those of their predictors in 1,091 Brown Swiss cows reared on 85 farms in order to assess the potential of using EME-related phenotypes in selective breeding. Univariate and bivariate genetic models were fitted in a Bayesian framework. The means of the marginal posterior distribution of intra-herd heritability ranged from 0.12 for estimated methane production (g/d/cow) to 0.24 for estimated methane yield (g/kg dry matter intake DMI), with intermediate values for estimated methane intensity, increasingly higher when expressed per kg of corrected milk (0.13), fresh cheese (0.16), or cheese solids (0.20). Regarding the correlations, the milk quality traits and percentage cheese yields were generally moderately correlated with the estimated EME traits, and were variable in terms of sign. Daily milk and cheese yield traits were, as expected, all highly positively correlated with estimated daily methane production. In contrast, they were negatively correlated with estimated methane yield and intensity, the estimates being large in the case of phenotypic and herd correlations, and low in the case of additive genetic and residual correlations. With the exception of the negative correlations with daily methane production, EME traits exhibited trivial correlations with body size and BCS of cows, which, in turn, were negatively correlated with milk yield. Although the results should be validated on a larger population and different breeds, our study demonstrate the presence of additive genetic variation of EME traits, which could be exploited in breeding programmes for the improvement in both milk production and the ecological footprint of dairy farming. Highlights Enteric methane emissions (EME) of dairy cows can be estimated on the basis of milk fatty acid profile. EME exhibited exploitable genetic variation. Genetic selection could be preferentially based on predicted methane intensity per kg of milk, or per kg of cheese in countries where milk production is used mainly for cheese-making.