AbstractStrong, extensive magnetic fringe fields are a significant problem with magnetic resonance imaging magnets. This is particularly acute with 4‐T, whole‐body research magnets. To date this problem has been addressed by restricting an extensive zone around the unshielded magnet or by placing external unsaturated iron shielding around the magnet. This paper describes a solution to this problem which uses superconducting coils closely integrated with fully saturated iron elements. A 4‐T, 30‐cm‐bore prototype, based on this design principle, was built and tested. The 5 G fringe field is contained within 1 meter of the magnet bore along thezaxis. Homogeneity of the raw magnetic field is 10 ppm over 30% of the magnet's diameter after passive shimming. Compared with an unshielded magnet, 20% less superconductor is required to generate the magnetic field. Images and spectra are presented to demonstrate the magnet's viability for magnetic resonance imaging and spe