For discrete-time input-constrained systems, the notion of directionality is defined, and an optimal directionality compensator is presented. According to the definition, a single-input single-output (SISO) process may exhibit the directionality. Two examples of such processes are given and simulated. Given a controller output, the compensator calculates an optimal constrained (feasible) process input that results in a process response as 'close' as possible to the response of the process to the controller output. The compensator can be used for both linear and nonlinear processes, irrespective of the type of controller being used. For processes whose nonsingular characteristic (decoupling) matrix is independent of manipulated inputs and can be made diagonal by row or column rearrangements, the optimal directionality compensation is identical to clipping; this class of processes does not exhibit the directionality over very short time horizons. By three examples the performance of the optimal directionality compensator is shown and compared with those of clipping and direction preservation.