Significance The livestock sector contributes significantly to global warming through greenhouse gas (GHG) emissions. At the same time, livestock is an invaluable source of nutrition and livelihood for millions of poor people. Therefore, climate mitigation policies involving livestock must be designed with extreme care. Here we demonstrate the large mitigation potential inherent in the heterogeneity of livestock production systems. We find that even within existing systems, autonomous transitions from extensive to more productive systems would decrease GHG emissions and improve food availability. Most effective climate policies involving livestock would be those targeting emissions from land-use change. To minimize the economic and social cost, policies should target emissions at their source—on the supply side—rather than on the demand side.