MRI phase images are increasingly used, for example for Susceptibility Mapping, and distortion correction in functional and diffusion MRI. However, measured phase images contain wraps, because the phase is defined only between 0 and 2π. PRELUDE is the current gold-standard method for robust, 3D, spatial phase unwrapping, but its computation time can become very long (e.g. 10 hours), especially at high field and outside the brain. Here, we developed a new method, SEGUE, that produced similar results to PRELUDE in multi-echo brain and head-and-neck images, successfully unwrapped some regions where PRELUDE failed and was between 1.6 and 83 times faster.