In the last decade, several countries have included feed efficiency (as residual feed intake; RFI) in their breeding goal. Recent studies showed that RFI is favorably correlated with methane emissions. Thus, selecting for lower emitting animals indirectly through RFI could be a short-term strategy in order to achieve the intended reduction set by the EU Commission (-55% for 2030). The objectives were to 1) estimate genetic parameters for six methane traits, including genetic correlations between methane traits, production, and feed efficiency traits, 2) evaluate the expected correlated response of methane traits when selecting for feed efficiency with or without including methane, 3) quantify the impact of reducing methane emissions in dairy cattle using the Danish Holstein population as an example. A total of 26,664 CH breath records from 647 Danish Holstein cows measured over 7 years in a research farm were analyzed. Records on dry matter intake (DMI), body weight (BW), and energy corrected milk (ECM) were also available. Methane traits were methane concentration (MeC, ppm), methane production (MeP; g/d), methane yield (MeY; g CH/kg DMI), methane intensity (MeI; g CH/kg ECM), residual methane concentration (RMeC), residual methane production (RMeP, g/d), and two definitions of residual feed intake with or without including body weight change (RFI1, RFI2). The estimated heritability of MeC was 0.20 ± 0.05 and for MeP, it was 0.21 ± 0.05, whereas heritability estimates for MeY and MeI were 0.22 ± 0.05 and 0.18 ± 0.04, and for the RMeC and RMeP, they were 0.23 ± 0.06 and 0.16 ± 0.02, respectively. Genetic correlations between methane traits ranged from moderate to highly correlated (0.48 ± 0.16-0.98 ± 0.01). Genetic correlations between methane traits and feed efficiency were all positive, ranging from 0.05 ± 0.20 (MeI-RFI2) to 0.76 ± 0.09 (MeP-RFI2). Selection index calculations showed that selecting for feed efficiency has a positive impact on reducing methane emissions' expected response, independently of the trait used (MeP, RMeP, or MeI). Nevertheless, adding a negative economic value for methane would accelerate the response and help to reach the reduction goal in fewer generations. Therefore, including methane in the breeding goal seems to be a faster way to achieve the desired methane emission reductions in dairy cattle.