Growth rate discontinuity modelling (GRDM) is an understudied technique for estimating the size of population shocks in low-data contexts. It projects exponentially within the intercensal interval containing a shock, allowing a one-time projection discontinuity that it attributes to the demographic impact, usually the death toll, of that shock. I provide the first review of GRDM’s assumptions and previous uses. I also attempt to externally validate the method against independently well-characterised estimates of the death toll of the 1918–19 influenza pandemic. I find that GRDM requires high precision in its inputs to an extent rarely possible in historical and low-data contexts, especially at subnational levels. The areas of study in which GRDM’s previous results have been very influential, namely the 1830s Trail of Tears, the 1864-70 Paraguayan War, the 1918-19 influenza pandemic, and the 1965-66 mass killings in Java, should reconsider the method’s contributions to their fields.