In this paper I use a new keynesian model with nominal price rigidity to analyze the behaviour of the Swiss CPI. In the model nominal price rigidity arises because prices are costly to change for the firms (menu costs). The model shows that, when a supply shock or a sector-related demand shock occurs, the adjustment of relative prices remains incomplete if nominal prices are sticky. Consequently, in the short run, inflation can be significantly influenced by a small number of big price changes. The Swiss CPI data is consistent with the theory. They also provide some evidence that prices are more rigid downwards than upwards.