This work provides a new approach for phase-lead/lag compensators to achieve the desired specifications of gain and phase margins for all-pole stable plants with time-delay. The stabilizing regions of lead/lag compensators are first determined in terms of a graphical stability criterion. These regions are drawn graphically, not to be calculated mathematically. Then. by defining appropriate functions relative to the requirements of gain and phase margins, the curves in the stabilizing regions satisfying the pre-specified gain and phase margins can be drawn, which gives the complete information on gain and phase margins. Illustrative examples are given to show the design procedure and to compare our method with other existing tuning rules. (C) 2008 Elsevier Ltd. All rights reserved.