Head pose is utilized to approximate a user's line-of-sight for real-time image rendering and interaction in most of the 3D visualization applications using head-mounted displays (HMD). The eye often reaches an object of interest before the completion of most head movements. It is highly desirable to integrate eye-tracking capability into HMDs in various applications. While the added complexity of an eyetracked-HMD (ET-HMD) imposes challenges on designing a compact, portable, and robust system, the integration offers opportunities to improve eye tracking accuracy and robustness. In this paper, based on the modeling of an eye imaging and tracking system, we examine the challenges and identify parametric requirements for video-based pupil-glint tracking methods in an ET-HMD design, and predict how these parameters may affect the tracking accuracy, resolution, and robustness. We further present novel methods and associated algorithms that effectively improve eye-tracking accuracy and extend the tracking range.