We present algorithms for optimal harmonic disturbance attenuation in standard discrete-time control structure, based on a parametrisation of (marginally) stabilising controllers. The Frobenius norm and the spectral norm of the closed-loop transfer matrix at the disturbance frequencies are minimised. If there is only one frequency of the disturbance, the controller has an observer-based form, which we obtain by solving a static output feedback (SOF) stabilisation control problem. Although the SOF stabilisation problem is hard, the generical case of nonsquare matrix G(22) is solved by linear algebra methods. Numerical simulation results are presented. As a corollary, we transform the control problem with unit circle invariant zeros into a H-infinity control problem without such zeros. The elimination of the unit circle invariant zeros is based on the fact that matrix Y(zI - A + BF)(-1) is stable, where (Y, F) with Y >= 0 is a solution of a discrete-time algebraic Riccati system.