Susceptibility Mapping (QSM) is increasingly applied in parts of the body where fatty tissue is present. QSM uses the phase of the complex MRI signal which contains both susceptibility-, and chemical-shift-induced components. For accurate QSM, the latter need to be suppressed. Here we compared a range of different fat-correction strategies for QSM in head-and-neck images. Techniques providing reliable fat-fraction maps also gave similar susceptibility values in fatty fascia. However, some of these methods were not robust to the choice of echo times. In-phase imaging was found to be the best candidate for robust fat-correction in QSM of the head-and-neck.