When using quasi-differenced data in a model where a break in the intercept is allowed, asymptotic distributions of the M, ADF, and PT statistics are the same as those in the model where only an intercept and a time trend are included. However, the finite sample behaviour for common sample sizes used in empirical applications is very different. Finite-sample critical values are calculated using two different methods to select the break point and the lag length. Comparison with asymptotic and finite-sample distributions of a model, where only a constant and a time trend are included in the set of deterministic components, shows strong differences. In particular, these differences are more clear for the M and PT statistics, whereas the ADF statistics is not affected too much. An empirical application is performed to show the pitfalls of using asymptotic or finite-sample critical values for a model where a break in the intercept has not been taken into account.