This paper focusses on the energy-efficient control of a cable-driven robot for tasks that only require precise positioning at few points in their motion, and where that accuracy can be obtained through contacts. This includes the majority of pick-and-place operations. Knowledge about the task is directly taken into account when specifying the control execution. The natural dynamics of the system can be exploited when there is a tolerance on the position of the trajectory. Brakes are actively used to replace standstill torques, and as passive actuation. This is executed with a hybrid discrete-continuous controller. A discrete controller is used to specify and coordinate between subtasks, and based on the requirements of these specific subtasks, specific, robust, continuous controllers are constructed. This approach allows for less stiff and thus saver, and cheaper hardware to be used. For a planar pick-and-place operation, it was found that this results in energy savings of more than 30%. However, when the payload moves with the natural dynamics, there is less control of the followed trajectory and its timing compared to a traditional trajectory-based execution. Also, the presented approach implies a fundamentally different way to specify and execute tasks.