This paper assesses the Layard et al. (1991) NAIRU framework for explaining unemployment. Their approach is distinct from the natural rate of unemployment framework in that it postulates a short-run NAIRU influenced by 'hysteresis'. It is pointed out that this is not hysteresis in the meaning employed elsewhere, so an outline of what hysteresis actually implies for unemployment is offered. The main implication is that unemployment does not revert to a long-run 'natural rate' equilibrium, as claimed by Layard et al., but instead is shaped by the past extrema of dominant exogenous shocks. It is argued that this is a more useful approach to the explanation of equilibrium unemployment than the NAIRU, which, for its analytical and empirical flaws, can be considered to be 'not an interesting rate of unemployment'. The hysteretic alternative to the natural rate hypothesis can be called the DESIRU (dominant extrema, steady inflation, rate of unemployment).