A generic method for designing a 2-periodic controller for the simultaneous placement of the closed-loop poles of two single-input-single-output discrete shift-invariant plants at the origin is presented. The method consists of first recasting the simultaneous pole-placement problem as one of solving a coupled pair of linear polynomial equations involving three unknown polynomials, and then obtaining the controller parameters in terms of the coefficients of these polynomials. The isolated cases for which such pole placement is not possible have been listed. Simulation results show that the performances of systems thus compensated are superior to their performances when compensated using the higher periodicity controllers suggested in literature.