Two alternatives to Enders and Lee, 2012a and Enders and Lee, 2012b Fourier unit root testing strategy, which incorporates pretesting for nonlinearity, are considered. One is based on the union of rejection (UR) approach, and the other is a hybrid strategy that combines the UR approach with the use of extra information from nonlinearity pretesting. Simulation results show that the two proposed strategies, especially the hybrid, frequently outperform the original pretesting strategy.