The microwave spectrum of the unstable molecule sulphur difluoride, SF2, prepared via a pulsed electric discharge in an SF6/OCS mixture, has been measured using a pulsed jet cavity Fourier transform spectrometer. F-19 hyperfine structure has been resolved, and unusually small, negative values have been determined for two of the spin-rotation coupling constants. These constants have been used to calculate the 19F principal, inertial axis nuclear shielding components; the determined paramagnetic shieldings are also unusual and produce a large positive average shielding, sigma(av). The shieldings have been compared with the corresponding constants obtained for OF2, SiF2, and GeF2. The results for SF2 are consistent with values determined from earlier NMR experiments and ab initio calculations. The origin of the unusual shieldings has been found, and is discussed, using a semi-quantitative model, in terms of the geometry and the electronic energy level structure of the molecule.