Recent studies found evidence for nominal wage rigidity during periods of relatively high nominal GDP growth. It has been argued, however, that in an environment with low nominal GDP growth, when nominal wage cuts become customary, workers' opposition to nominal cuts would erode and, hence, firms would no longer hesitate to reduce nominal pay. If this argument is valid nominal wage rigidity is largely irrelevant because in a high-growth environment there is little need to cut nominal pay while in a low-growth environment the necessary cuts would occur. To examine this argument we use data from Switzerland where nominal GDP growth has been very low for many years in the 1990s. We find that the rigidity of nominal wages is a robust phenomenon that does not vanish in a low growth environment. In addition, it constitutes a considerable obstacle to real wage adjustments. In the absence of downward nominal rigidity, real wages would indeed be quite responsive to unemployment. Moreover, the wage sweep-ups caused by nominal rigidity are strongly correlated with unemployment suggesting that downward rigidity of nominal wages indeed contributes to unemployment.