Previous works by the authors [Wei et al., 2003; 2004] have developed a simple bearing-only control law for a mobile robot with demonstrated convergence to a unique final pose and orientation. Here, we use a time-varying weight strategy to first draw the robot towards a known “good” starting region and then a second set of weights is used for docking. This strategy allows the robot to dock successfully from a wider range of initial positions. Experimental results demonstrate the method and show an unexpected bonus: the docking accuracy achieved is significantly better than the previous approaches.