This paper presents a graphical method for locating the optimum position of outriggers on shear walls with basement fin extensions for preliminary design of high-rise stuctures subjected to horizontal loading. This location for the outrigger will cause a maximum reduction in lateral deflection at the top of the building. The method requires the input of seven structural parameters: bending stiffnesses for the shear wall, outrigger and fin-walls, racking shear stiffness of the outrigger, an overall bending stiffness contribution from the exterior columns, and rotational stiffnesses for the shear wall and column foundations. These parameters allow the setting up of two compatibility equations for rotations at the intersections of the neutral ...