We show that the use of generalized least squares (GLS) detrending procedures leads to important empirical power gains compared to ordinary least squares (OLS) detrending method when testing the null hypothesis of unit root for bounded processes. The non-centrality parameter that is used in the GLS-detrending depends on the bounds, so that improvements on the statistical inference are to be expected if a case-speci.c parameter is used. This initial hypothesis is supported by the simulation experiment that has been conducted.