In surveys persons have a tendency to round their answers. For example, in the Labour Force Survey people are asked about the period they have been unemployed. There is clearly a tendency to give answers that are rounded to years of half years. Because of this rounding statistics based on this data tend to be biased. In this paper we introduce a method with which the rounding mechanism is modelled together with the ‘true’ underlying distribution. These are then used to select samples which are likely to be rounded an impute new values for these. This method is applied to the Labour Force Survey data. An investigation of robustness shows that the method is robust against misspecification of the model of the underlying distribution and to misspecification of the rounding mechanism.