This document proposes that greenhouse gases (GHGs) can be divided into two categories for the purpose of limiting global temperature rise to 2°C: 1) "Long-lived" GHGs such as CO2, whose contribution to peak temperature rise is determined by their total cumulative emissions over time. 2) "Shorter-lived" GHGs such as methane, whose contribution depends on sustained emissions levels. The document shows through modeling that summing the impacts of these two GHG categories provides a way to estimate peak temperature that reduces reliance on arbitrary time horizons. This approach could form the basis for a multi-gas emissions policy framework aimed at staying below the 2°C limit.