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Prediction of carbon monoxide (CO) emission is critical in gas turbine combustion. Compact yet accurate reaction mechanisms are required to predict CO with reasonable computing cost. This study uses SHERPA optimization algorithm to optimize the kinetic rate parameters of a 3-step methane-air global reaction mechanism for improved CO predictions. DARS is used as the chemical kinetics solver. Freely propagating laminar flame and constant pressure reactor solutions with GRI-Mech 3.0 reaction mechanism are used as references for optimization. Tradeoffs in the choice of solution techniques and solver settings for fast and accurate design runs are discussed in the paper. Optimization results and their interpretation for improving the design study is also presented. The optimal results show significant improvements in predictions compared to the baseline case. The workflow and best practices presented in this paper may be extended to optimize global reaction mechanisms for any given range of operating conditions.