Nominal wage rigidity has been shown to exist in periods of high inflation, while reduction in nominal pay has been hypothesized to occur in times of low inflation. Nominal wage rigidity would therefore become irrelevant because there is little need to cut nominal pay under high inflation, while the necessary cuts would occur under low inflation. We test this hypothesis by examining Swiss data in the 1990s, where wage inflation was low. Nominal wage rigidity proves robust in a low inflation environment, constituting a considerable obstacle to real wage adjustments. Real wages would indeed respond to unemployment without downward nominal rigidity. Moreover, wage sweep-ups caused by nominal rigidity correlate strongly to unemployment, suggesting downward nominal wage rigidity fuels unemployment.