Climate change mitigation requires the reduction of greenhouse gas (GHG) emissions. The majority of the discussions on climate change policy focus exclusively on the reduction of carbon dioxide (CO2) emissions but ignore other important GHGs such as methane. This paper investigates the optimal choice of policy instruments under the joint consideration of CO2 and methane in a dynamic setting with asymmetric information and pollutant correlations. We develop a dynamic programming model with two state variables and calibrate it to the global warming case. The results show that it is optimal to levy tax on both CO2 and methane. A mixed strategy that implements a tax on CO2 and a quota on methane is the second-ranked choice.