In this paper we consider the proportional-integral (PI) controller and the problem of modern design using gain margin, phase margin and bandwidth as simultaneous specifications. We develop analytical approaches to deal with these specifications leading to the generation of a design surface which displays all achievable designs as well as the various tradeoffs inherent to the problem. The key supporting results are the computation of the stabilizing set and the magnitude and phase loci of the PI controller. The results are illustrated by examples of two specially chosen transfer functions and an application to voltage regulation in a boost converter, where interval polynomials were included to cope with variations in the supply source.