We propose that automatically adjusting the scale factor in rate-control teleoperation could enable a human operator to better control the motion of a remote robot. In this paper, we present four new variable-scaling rate-control methods that adjust the scale factor depending on the state of the user's input commands and/or the risk of a collision between the robot and its environment. Methods that depend on the risk of a collision are designed to guarantee collision avoidance by setting the scale factor to be zero if the operator issues a command that would result in a collision between the robot and its environment. A within-subject user study was conducted to determine the effects of the four newly designed rate-control methods and a traditional fixed-scale rate-control method on a person's ability to complete a navigation task in a simulated two-dimensional environment. The results of this study indicate that well-designed variable-scale rate control can guarantee collision-free teleoperation without reducing task efficiency.