• Olive cake in the diet has a mitigation effect on enteric CH 4 production in sheep. • Dry-matter intake and the digestible fraction of structural carbohydrates are reliable enteric CH 4 emission predictors. • The average Y m value proposed by IPCC (2019) overestimates CH 4 emission rates for sheep in semiarid to arid ecosystems. Methane production was individually measured, using open-circuit respiration chambers, in Segureña wethers fed diets including two different levels of olive cake (OC) sprayed with soda solutions to attain 0, 5, 7.5 and 10 g NaOH/100 g OC. Increasing level of OC in diet reduced (P < 0.001) CH 4 production (from 3.34 to 2.37 % of total ingested carbon and from 8.97 to 7.90 % of total digestible energy intake), which represent reductions in energy losses of up to 12 % of the digestible energy (DE) intake. Differences ( P ≤ 0.001−0.002) in enteric CH 4 production due to treatment of OC with alkali were observed. The average value for the rate of conversion of feed energy to CH 4 energy (Y m ) was 5.96 kJ/100 kJ GE intake or 8.97 kJ/100 kJ DE for the standard basal diets, containing 100 g OC/kg diet. Increasing OC in the basal diet to achieve 400 g/kg diet resulted in a substantial reduction of enteric CH 4 production promoting a Y m value of 4.18 kJ CH 4 /100 kJ GE or 7.90 kJ CH 4 /100 kJ DE intake. A decrease ( P = 0.018) in enteric CH 4 production (l/kg DMI) due to the alkali treatment of OC was noticed. Accurate predictions of CH 4 production were obtained by simple regressions equations relating measured values of CH 4 production and diets composition and/or intake. Dry matter intake and structural carbohydrates content in the diet were accurate predicting factors of the enteric CH 4 production. The best correlations were obtained when enteric CH 4 yield (CH 4 , l/kg DMI) was the variable to be estimated.