A shielded superconducting MRI magnet system uses a multi-layer shielded coil design. By splitting the magnet coils into a plurality of coil layers, an increased number of degrees of freedom is achieved which, in turn, permits minimization of the overall length of the magnet while nevertheless avoiding excessive magnet field and stress values in the coils. A compact coil system is thereby designed which also satisfies the plurality of MRI requirements with regard to sufficiently large investigational volume, magnet field strength, acceptable homogeneity, and magnet stray field limitation while achieving sufficiently low maximum coil B field strengths and stress values to avoid quenches and maintain the structural integrity of the magnet.