A simple tandem-mirror coil system is found which has the property that the geodesic curvature of the paraxial magnetic field is locally small everywhere. This design approaches the ideal of a 'locally omnigenous' configuration in which the particle drift surfaces coincide with the magnetic flux surfaces. Thus, radial losses due to resonant ion and stochastic radial diffusion are minimized. Plasma distortion due to central-cell parallel currents and instability due to trapped particles are also greatly reduced. The advantages and disadvantages of the design for reactor applications are discussed.