We present an effective way to combine the information provided by edges and by feature points for the purpose of robust real-time 3-D tracking. This lets our tracker handle both textured and untextured objects. As it can exploit more of the image information, it is more stable and less prone to drift that purely edge or feature-based ones. We start with a feature-point based tracker we developed in earlier work and integrate the ability to take edge-information into account. Achieving optimal performance in the presence of cluttered or textured backgrounds, however, is far from trivial because of the many spurious edges that bedevil typical edge-detectors. We overcome this difficulty by proposing a method for handling multiple hypotheses for potential edge-locations that is similar in speed to approaches that consider only single hypotheses and therefore much faster than conventional multiple-hypothesis ones. This results in a real-time 3-D tracking algorithm that exploits both texture and edge information without being sensitive to misleading background information and that does not drift over time.