The key factor in reducing the consumed energy when dependent-tasks applications are scheduled on DVFS-enabled computing platforms is task execution time slots. The unique and axiomatic approach to reduce the energy consumption on such platforms involves scaling down the execution frequency of each task within its execution time slot, provided a suitable scaling-down frequency is available. Regrettably, scheduling algorithms often shrink task execution time slots due to minimizing task completion times. This paper presents BlueMoon, a mechanism that reschedules the application tasks to extend the execution time slot of each task while ensuring that the overall completion time of the application tasks remains unaffected. BlueMoon is implemented and tested on numerous schedules of application graphs. The experimental results, conducted through computer simulations, demonstrate that BlueMoon substantially extends the execution time slots of tasks when compared to other mechanisms.