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A simple modification of a standard tandem mirror coil design is shown to significantly improve the radial confinement of particles without sacrificing interchange stability. In the new design, the local departure of the particle drift surfaces from the vacuum flux surface is small everywhere, thereby reducing radial particle losses. This is achieved by adjusting the coil parameters to approximate the transport-minimizing magnetic field profiles of Myra et al. near the magnetic axis. Using this technique as a guide, a family of coil configurations is studied. It is shown that reducing the elliptical fanning of the flux surfaces on the inboard side of each quadrupole anchor leads to a great reduction in the radial transport.