A notion of process directionality in input-constrained processes is defined, and the class of processes that do not exhibit the process directionality is characterized. An optimal directionality compensator for non-linear processes with actuator saturation non-linearities is presented. Given an unconstrained controller output and the characteristic (decoupling) matrix of the process under consideration, the compensator calculates an optimal constrained (feasible) process input that results in a process response as 'close' ars possible to the response of the same process to the unconstrained controller output. The compensator can be used for both linear and non-linear processes, irrespective of the type of controller being used. For processes whose non-singular characteristic matrix can be made diagonal by row or column rearrangements, the optimal directionality compensator is identical to a series of limiters (clippers); this class of processes does not exhibit the process directionality over a short time horizon. The performance of the optimal directionality compensator is shown and compared with those of clipping and direction preservation, by numerical simulation of a linear example under decentralized proportional-integral control, a linear example under model-based control, and a non-linear bioreactor under input-output linearizing control.