The homogeneity of the magnetic field of an Oxford 85/310HR magnet was optimized with the use of passive shims (i.e., pieces of steel) and room-temperature electronic shims. Both the characteristics of the passive shims and the current settings for the room-temperature electronic shims were calculated with the goal of minimizing field inhomogeneities as assessed by Fourier analysis of data from circular field plots. The measurement techniques, the methods of data analysis, and the techniques employed in correcting the magnetic field are presented. Difficulties and constructive approaches are suggested in these descriptions. The final results show a field of excellent homogeneity over a 10-cm-diameter spherical volume, with a peak-to-peak variation of 3.2 ppm, which is better than the manufacturer's expected specification of 5 ppm. A water-filled sphere of 10 cm diameter gave a half-height linewidth of 0.14 ppm after a small amount of additional touch-up shimming. The field homogeneity as corrected is much improved over its original state, allowing the acquisition of improved spectra from samples of a size several centimeters in each linear dimension. Thus the field homogeneity is more useful for in vivo spectroscopy, the purpose for which the magnet was intended.