High magnetic fields (≊20 kG) are realizable from spherical and cylindrical transverse field sources in relatively small structures (∼10 cm). In some applications where the working space is cylindrical and long compared to its diameter, these fields can be augmented by about 5 kOe without an increase in the outer dimensions of the original structures. In spherical sources, a similar procedure yields a field increase of approximately 3 kOe. A method is described whereby field distortions arising from access holes to the interiors of such magnet structures can be greatly reduced. Such options considerably enhance the range of applicability to millimeter/microwave and optical devices.