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The atmospheric lifetime and radiative impacts of different climate pollutants can both differ markedly, so metrics that equate emissions using a single scaling factor, such as the 100-year Global Warming Potential (GWP(100)), can be misleading. An alternative approach is to report emissions as 'warming-equivalents' that result in similar warming impacts without requiring a like-for-like weighting per emission. GWP*, an alternative application of GWPs where the CO2-equivalence of short-lived climate pollutant emissions is predominantly determined by changes in their emission rate, provides a straightforward means of generating warming-equivalent emissions. In this letter we illustrate the contrasting climate impacts resulting from emissions of methane, a short-lived greenhouse gas, and CO2, and compare GWP(100) and GWP* CO2-equivalents for a number of simple emissions scenarios. We demonstrate that GWP* provides a useful indication of warming, while conventional application of GWP(100) falls short in many scenarios and particularly when methane emissions are stable or declining, with important implications for how we consider 'zero emission' or 'climate neutral' targets for sectors emitting different compositions of gases. We then illustrate how GWP* can provide an improved means of assessing alternative mitigation strategies. GWP* allows warming-equivalent emissions to be calculated directly from CO2-equivalent emissions reported using GWP(100), consistent with the Paris Rulebook agreed by the UNFCCC, on condition that short-lived and cumulative climate pollutants are aggregated separately, which is essential for transparency. It provides a direct link between emissions and anticipated warming impacts, supporting stocktakes of progress towards a long-term temperature goal and compatible with cumulative emissions budgets.