In this paper we conduct a simulation experiment to quantitatively assess the impacts of reallocating budgetary resources within Pillar 1 of the Common Agricultural Policy (CAP) from direct income support to a direct greenhouse gas (GHG) reduction subsidy for EU farmers. Although such a budgetary shift is not foreseen in the current political discussions on the future CAP post 2020, the analysis is motivated by calls for both an increased contribution from the agricultural sector to combat global warming, and a more incentive-based delivery system for direct payments. For the analysis, we apply a partial equilibrium model for the agricultural sector (CAPRI) covering both the EU farming sector with high geographical detail as well as global food commodity markets. An integrated emission accounting for EU agriculture and global agri-food products, as well as optional technological GHG mitigation options for EU farmers make CAPRI specifically suitable for the impact assessment. For the scenario we assess a policy that removes the basic direct payments under Pillar 1 of the current CAP and provides farmers a GHG-saving subsidy instead, without increasing the total budget for direct payments. A major empirical contribution of the paper is the calculation of budget-neutral subsidy rates for the hypothetical GHG-reduction subsidy, factoring in farmers' supply and technology-adjusting responses to the policy change. The subsidy rates are derived by combining the regional representative farm models of CAPRI with a Newton-Raphson numerical approximation method that guarantees budget-neutrality. We find that a budget-neutral re-allocation of financial resources towards subsidized emission savings can reduce agricultural non-CO2 emissions by 21% in the EU by 2030, compared to a business-as-usual baseline. Almost two-thirds of the EU emission savings are due to production decreases, and, therefore, part of this GHG reduction is threaten to be offset globally by emission leakage effects. At the aggregated level, the emission-saving subsidy and increased producer prices compensate farmers for the foregone direct income support, but the significant regional differences indicate both an accelerated structural change and heterogeneous income effects in the farm population. We conclude that the assumed regional budget-neutrality condition introduces inefficiencies in the incentive system, and the full potential of the EU farming sector for GHG emissions reduction is not reached in the scenario; leaving ample room for the design of more efficient agricultural policies to combat global warming.