In this paper, frequency-domain design methods for discrete-time PI, PD, and PID controllers are proposed. Design requirements are specified in terms of the desired crossover frequency and phase margin, as they are related to settling time and overshoot, respectively. The method allows design requirements to be achieved directly because it involves only a few steps, and its application only requires a Bode plot. It also allows the stability limits of control systems to be analyzed only by observing the plant’s Bode plot. Simulations were performed, comparing PI, PD, and PID controllers.