Multi-gas climate agreements require a metric by which emissions of gases with different lifetimes and radiative properties can be placed on a common scale. The Kyoto Protocol to the United Nations Framework Convention on Climate Change uses the global warming potential (GWP) as such a metric. The GWP has attracted particular criticism as being inappropriate in the context of climate policy which seeks to restrict warming below a given target, because it gives equal weight to emissions irrespective of the target and the proximity to the target. The use of an alternative metric, the time-dependent global temperature change potential (GTP), is examined for its suitability and the prospects for it including very short-lived species. It retains the transparency and relative ease of use, which are attractive features of the GWP, but explicitly includes a dependence on the target of climate policy. The weighting of emissions using the GTP is found to be significantly dependent on the scenarios of future emissions and the sensitivity of the climate system. This may indicate that the use of any GTP-based weighting in future policymaking would necessitate regular revisions, as the global-mean temperature moves towards a specified target.