A discrete coil EIT system is investigated for the general case of an eccentric circular inhomogeneity. The solution methodology of the forward problem of this system is explained. An optimization procedure using this forward problem solution is developed to rind optimum currents that maximize the distinguishability. For an eccentric inhomogeneity problem, it is shown that the coil currents can be optimized to focus the current density in a region of interest. Optimum coil currents under limited peak coil currents constraint and limited total power constraint are obtained. Representative examples that demonstrate the performance of the system are presented.