A systematic study of magnetic designs has been carried out for three-cell choke coil quadrupole-stabilized tandem mirror reactors, comparable in size to the (octopole) MINIMARS design. In these designs, a single-mirror cell at each end of the machine serves as an end plug, thermal barrier, and magnetohydrodynamic anchor. The multiple functions of the end plugs make it difficult to simultaneously optimize the physics properties of the plasma (stability, radial confinement, and good particle drift orbits). Two different design approaches have been studied using recently developed magnetic optimization techniques. Typical physics figures of merit are given and critical issues discussed for each design. When the various constraints associated with the high-field choke coil are taken into account, it is found that an acceptable design is beyond the reach of present technology.