The Australian sheep industry aims to increase the efficiency of sheep production by decreasing the amount of feed eaten by sheep. Also, feed intake is related to methane production, and more efficient (low residual feed intake) animals eat less than expected. So we tested the hypothesis that more efficient sheep produce less methane by investigating the genetic correlations between feed intake, residual feed intake, methane, carbon dioxide, and oxygen. Feed intake, methane, oxygen, and carbon dioxide were measured on Merino ewes at postweaning (1,866 at 223 d old), hogget (1,010 sheep at 607 d old), and adult ages (444 sheep at 1,080 d old). Sheep were fed a high-energy grower pellet ad libitum for 35 d. Individual feed intake was measured using automated feeders. Methane was measured using portable accumulation chambers up to 3 times during this feed intake period. Heritabilities and phenotypic and genotypic correlations between traits were estimated using ASReml. Oxygen (range 0.10 to 0.20) and carbon dioxide (range 0.08 to 0.28) were generally more heritable than methane (range 0.11 to 0.14). Selecting to decrease feed intake or residual feed intake will decrease methane (genetic correlation [] range 0.76 to 0.90) and carbon dioxide ( range 0.65 to 0.96). Selecting to decrease intake ( range 0.64 to 0.78) and methane ( range 0.81 to 0.86) in sheep at postweaning age would also decrease intake and methane in hoggets and adults. Furthermore, selecting for lower residual feed intake ( = 0.75) and carbon dioxide ( = 0.90) in hoggets would also decrease these traits in adults. Similarly, selecting for higher oxygen ( = 0.69) in hoggets would also increase this trait in adults. Given these results, the hypothesis that making sheep more feed efficient will decrease their methane production can be accepted. In addition, carbon dioxide is a good indicator trait for feed intake because it has the highest heritability of the gas traits measured; is cheaper, faster, and easier to measure than feed intake and has strong phenotypic and genetic correlations with feed intake. Furthermore, selection for feed intake, feed efficiency, methane, and carbon dioxide can be done early in sheep at postweaning age or hoggets. This early selection reduces the generation interval for breeding, thereby increasing response to selection.