In a magnetic resonance apparatus whose subject receiving bore (12) is short, e.g. has an axial length to diameter ratio of less than 1.75:1, typically about 1.67:1, harmonic distortions in a temporally constant magnetic field generated in the bore by superconducting magnets (10) surrounding the bore are reduced by placing shims in shim trays (80) disposed longitudinally around the bore (12). Each shim tray contains a number of shim pockets (84) which receive ferrous shims for shimming the magnetic field in the bore. An initialization system (60) calibrates the initial magnetic field within the bore. An initial shim distribution is determined which shims the inhomogeneous magnetic field toward a target more homogeneous magnetic field. An optimization system (66) determines a residual magnetic field from a difference between the present inhomogeneous magnetic field of the bore and the target magnetic field. The amounts of ferrous material assigned to the shim pockets are optimized in fractional groups to determine optimal shim settings to produce a shimming magnetic field equal to a negative of the residual magnetic field. In this manner, the net magnetic field is made substantially equal to the target homogeneous magnetic field.