This paper presents a novel system inversion approach to the set-point regulation of linear scalar minimum-phase systems. This approach uses closed-form expressions of cause/effect pairs that make possible an arbitrarily smooth transition between two given output set-points. The cause/effect pairs are based on the introduced concept of "transition" polynomials. Simple optimization procedures are then proposed to solve the relevant optimal output synthesis and optimal input synthesis. The potentiality of the method is highlighted by the examples presented, namely, a synthesis of elevator velocity profiles and the performance improving of a PID controller.