Summary: The finite-sample size properties of momentum-threshold autoregressive (MTAR) asymmetric unit root tests are examined in the presence of level shifts under the null hypothesis. The original MTAR test using a fixed threshold is found to exhibit severe size distortion when a break in level occurs early in the sample period, leading to an increased probability of an incorrect inference of asymmetric stationarity. For later breaks the test is also shown to suffer from undersizing. In contrast, the use of consistent-threshold estimation results in a test which is relatively robust to level shifts.