Large and spatially-linear phase errors along the frequency-encode direction may be induced by several common and hard-to-avoid system imperfections such as eddy currents. For data acquired in dual-echo Dixon techniques, the linear phase error can be more aggravated when compared to that acquired in a single echo and can pose challenges to a phase-correction algorithm necessary for successful Dixon processing. In this work, we propose a two-step process that first corrects the linear component of the phase errors with a modified Ahn-Cho algorithm (Ahn CB and Cho ZH, IEEE Trans. Med. Imaging 6:32, 1987) and then corrects the residual phase errors with a previously-developed region-growing algorithm (Ma J, Magn. Res. Med. 52:415, 2004). We demonstrate that successive application of the two-step process to data from a dual-echo Dixon technique provides a "1-2 punch" to the overall phase errors and can overcome local water and fat separation failures that are observed when the region-growing-based algorithm is applied alone.