This paper describes the algorithm used to point the high gain antennae on NASA/JPL's Mars Exploration Rovers. The gimballed antennae must track the Earth as it moves across the Martian sky during communication sessions. The algorithm accounts for (1) gimbal range limitations, (2) obstructions both on the rover and in the surrounding environment, (3) kinematic singularities in the gimbal design, and (4) up to two joint-space solutions for a given pointing direction. The algorithm computes the intercept-times for each of the occlusions and chooses the jointspace solution that provides the longest track time before encountering an occlusion. Upon encountering an occlusion, the pointing algorithm automatically switches to the other joint-space solution if it is not also occluded. The algorithm has successfully provided flop-free pointing for both rovers throughout the mission.