This paper presents a new method to correct for measurement error in wage data and applies this method to address an old question: How much downward wage flexibility is there in the United States? We apply standard methods developed by Bai and Perron to identify structural breaks in time series data. Applying these methods to wage histories allows us to identify when each person experiences a change in nominal wages. The length of the period of constant nominal wages is left unrestricted and is allowed to differ across individuals, as are the size and direction of the nominal-wage change. We apply these methods to data from the Survey of Income and Program Participation. The evidence we provide indicates that the probability of a cut in nominal wages is substantially overstated in data that are not corrected for measurement error.