The literature on metrics to measure contributions to climate change from emissions of different greenhouse gases divides into studies that highlight physical aspects and studies that show the importance of economic factors. This paper distinguishes the physical aspects and implications of economic factors by asking what is demanded from physically based metrics if used for a specific policy objective.We study the aim of maximizing the welfare of emissions generated by consumption when there is a limit to the increase in global mean temperature. In that case, metrics ought to change over time,with increasingweight on short-living gases before the temperature limit is met. Metrics for short-living gases increase also with increasing uncertainty. Adjustments to new information spur higher metrics for short-living gases if it reduces the expected allowable emissions before the target is met, and lower metrics in the opposite case. Under a binding target, metrics refer to the instantaneous impact on radiative forcing multiplied by the lifetime of the respective gases, and adjusted by the attitude to risk.