This paper uses Icelandic data to assess standard methods for estimating the natural rate of unemployment. Surprisingly, estimating the path of the natural rate of unemployment for the period 1990-1998 produces a natural-rate path that mirrors the path taken by actual unemployment. The paper goes on to show that this result is misleading for three reasons: First, the unemployment spells of low-income workers appear to have been partly voluntary and their unemployment therefore did not exert much downward pressure on wages and prices, nor did their reemployment at the end of the 1990s threaten price stability. Second, the influx of foreign workers during the recent boom reduced inflationary pressures. Taken together, the two effects caused the effective labour force to adjust to changes in the demand for labour, hence obscuring the relationship between inflation and unemployment over the cycle. In addition, there is an asymmetry in any effect unemployment may have on inflation in that wages and prices exhibit downward rigidity at low inflation rates. As a result, estimating the level of the natural rate of unemployment using data on inflation and unemployment tends to be misleading at low inflation rates.