The accommodation of conventional 2D GUIs with virtual environments (VEs) can greatly enhance the possibilities of many VE applications. In this paper we present a variation of the well-known ray-casting technique for fast and accurate selection of 2D widgets over a virtual window immersed into a 3D world. The main idea is to provide a new interaction mode where hand rotations are scaled down so that the ray is constrained to intersect the active virtual window. This is accomplished by changing the control–display ratio between the orientation of the user’s hand and the ray used for selection. Our technique uses a curved representation of the ray providing visual feedback of the orientation of both the input device and the selection ray. We have implemented this technique and evaluated its effectiveness in terms of performance and user preference. Our experiments on a four-sided CAVE indicate that the proposed technique can increase the speed and accuracy of component selection in 2D GUIs immersed into 3D worlds.