It is standard to model the output-inflation trade-off as a linear relationship with a time-invariant slope. We assess empirical evidence for three types of nonlinearity in the short-run Phillips curve. At an empirical level, we aim to discover why large negative output gaps in Japan during the period 1998-2002 did not lead to accelerating deflation, but instead coincided with stable, albeit moderately negative, inflation. We document that this episode is most convincingly interpreted as reflecting a gradual flattening of the Phillips curve. Our analysis sheds light on the determinants of the time- variation in the Phillips curve slope. Our results suggest that, in any economy where trend inflation is substantially lower (or substantially higher) today than in past decades, time-variation in the slope of the short-run Phillips curve has become too important to ignore.