A non-iterative method for the computation of the infimum for a class of discrete-time H-infinity optimal control problems, and the solvability conditions for the general discrete-time disturbance decoupling problem are given in this paper. The method for the computation of the infimum is applicable to systems where the transfer functions from the disturbance input to the measurement output and from the control input to the controlled output are free of unit circle invariant zeros and satisfy certain geometric conditions. The solvability conditions we obtained for the general discrete-time disturbance decoupling problem are also necessary and sufficient conditions.