Augmentative and alternative communication tools allow people with severe motor disabilities to interact with computers. Two commonly used tools are video-based interfaces and eye trackers. Video-based interfaces map head movements captured by a camera to mouse pointer movements. Alternatively, eye trackers place the mouse pointer at the estimated position of the user's gaze. Eye tracking based interfaces have been shown to even outperform traditional mice in terms of speed, however the accuracy of current eye trackers is not enough for fine mouse pointer placement. In this paper we propose the Head Movement And Gaze Input Cascaded (HMAGIC) pointing technique that combines head movement and gaze-based inputs in a fast and accurate mouse-replacement interface. The interface initially places the pointer at the estimated gaze position and then the user makes fine adjustments with their head movements. We conducted a user experiment to compare HMAGIC with a mouse-replacement interface that uses only head movements to control the pointer. Experimental results indicate that HMAGIC is significantly faster than the head-only interface while still providing accurate mouse pointer positioning.