Methane abatement and geoengineering have a short-lived effect on temperature compared with carbon abatement. Different optimal tax paths for these actions arise in a cost-benefit framework with an unknown temperature threshold where severe and irreversible climate impacts, called a tipping point, occurs. Tax paths are compared with a cost-minimising approach where an upper-temperature limit is set. In both approaches, the weight (ratio) of prices of short-lived gases to carbon prices converge to the same value by the end of the peak temperature stabilisation period. Numerical results from the cost-benefit framework suggest: the optimal weight for methane is close to the current United Nations policy of a 100-year Global Warming Potential, and the 100-year timeframe should decrease to align with the expected end of peak temperature. The use of geoengineering can lower the initial carbon tax and extend the life of the tax.