Due to associated hydrological risks, there is an urgent need to provide plausible quantified changes in future extreme rainfall rates. Convection-permitting (CP) climate simulations represent a major advance in capturing extreme rainfall and its sensitivities to atmospheric changes under global warming. However, they are computationally costly, limiting uncertainty evaluation in ensembles and covered time periods. This is in contrast to the Climate Model Intercomparison Project (CMIP) 5 and 6 ensembles, which cannot capture relevant convective processes, but provide a range of plausible projections for atmospheric drivers of rainfall change. Here, we quantify the sensitivity of extreme rainfall within West African storms to changes in atmospheric rainfall drivers, using both observations and a CP projection representing a decade under the Representative Concentration Pathway 8.5 around 2100. We illustrate how these physical relationships can then be used to reconstruct better-informed extreme rainfall changes from CMIP, including for time periods not covered by the CP model. We find reconstructed hourly extreme rainfall over the Sahel increases across all CMIP models, with a plausible range of 37%–75% for 2070–2100 (mean 55%, and 18%–30% for 2030–2060). This is considerably higher than the +0–60% (mean +30%) we obtain from a traditional extreme rainfall metric based on raw daily CMIP rainfall, suggesting such analyses can underestimate extreme rainfall intensification. We conclude that process-based rainfall scaling is a useful approach for creating time-evolving rainfall projections in line with CP model behaviour, reconstructing important information for medium-term decision making. This approach also better enables the communication of uncertainties in extreme rainfall projections that reflect our current state of knowledge on its response to global warming, away from the limitations of coarse-scale climate models alone.