GWP* was recently proposed1 as a simple metric for calculating warming-equivalent emissions by equating a change in the rate of emission of a short-lived climate pollutant (SLCP) to a pulse emission of carbon-dioxide. Other metrics aiming to account for the time-dependent impact of SLCP emissions, such as CGWP, have also been proposed2. In 2019 an improvement to GWP* was proposed by Cain et al3, hereafter CLA, combining both the rate and change in rate of SLCP emission, justified by the rate of forcing decline required to stabilise temperatures following a recent multi-decade emissions increase. Here we provide a more direct justification of the coefficients used in this definition of GWP*, with a small revision to their absolute values, by equating CO2 and SLCP forcing directly, without reference to the temperature response. This provides a more direct link to the impulse-response model used to calculate GWP values and improves consistency with CGWP values.