The post-pandemic inflationary surge again challenged our views on the Phillips curve. International evidence that the Phillips curve is non-linear is supported by micro-evidence that agents are attentive to inflation once it passes a threshold. Beyond this threshold, inflation expectations are slow to fall, steepening the Phillips curve. Using a self-exciting threshold autoregressive model, we determine that the slope of the Phillips curve in South Africa is state dependent (2000–2024). The threshold is best described as a range between 4.28% and 9.29%, with a mean of 5.55%. We find low-inflation regimes to be self-stabilising as the probability of remaining in this regime exceeds the probability of transitioning to a high-inflation regime. Our findings have implications for discussions about the appropriate level of the inflation target. We recommend that the inflation target should fall low enough that a routine-sized supply shock does not push inflation deep into the threshold range (red zone). Considering the size of oil price shocks typically experienced in South Africa, we argue that a target of 3.37% would be just low enough to offer a buffer to accommodate the direct effect of standard-sized shocks without entering the red zone. Our results therefore support the position of Honohan and Orphanides (2022) that the South African Reserve Bank should target inflation of 3%.