This paper provides new insight into the relationship between inflation and consumer price setting by examining a large data set of Mexican consumer prices covering episodes of both low and high inflation, as well as the transition between the two. Overall, the economy shares several characteristics with time-dependent models when the annual inflation rate is low (below 10-15%), while displaying strong state dependence when inflation is high (above 10-15%). At low inflation levels, the aggregate frequency of price changes responds little to movements in inflation because movements in the frequency of price decreases partly offset movements in the frequency of price increases. When the annual inflation rate rises beyond 10-15 percent, however, there are no longer enough price decreases to counterbalance the rising occurrence of price increases, making the frequency of price changes more responsive to inflation. It is shown that a simple menu-cost model with idiosyncratic technology shocks predicts remarkably well the level of the average frequency and magnitude of price changes over a wide range of inflation.