The empirical powers of recently proposed threshold cointegration tests are examined. Using an empirically realistic data generation process two crucial results are derived. First, relative to the implicitly symmetric Engle–Granger test, threshold cointegration tests lack power even in the presence of substantial asymmetry. Second, the use of consistent-threshold estimation to endogenise or optimize threshold selection is found to reduce the power of both threshold autoregressive and momentum threshold autoregressive cointegration tests. The implications of these findings are noted in light of the increased use of threshold cointegration tests in recent empirical research in economics and finance.