Scheduling dependent tasks is one of the most challenging problems in parallel and distributed systems. It is known to be computationally intractable in its general form as well as several restricted cases. An interesting application of scheduling is in the area of energy awareness for mobile battery operated devices where minimizing the energy utilized is the most important scheduling policy consideration. A number of heuristics have been developed for this consideration. In this paper, we study the scheduling problem for a particular battery model. In the proposed work, we show how to enhance a well know approach of accounting for the slack generated at runtime due to the difference between WCET (Worst Case Execution Time) and AET (Actual Execution Time). Our solution exploits the fact that even though some tasks become available based on the actual periodicity of a task they are not executed because the run queue is determined by the schedule generated in the offline phase I of the algorithm using the conservative EDF (Earliest Deadline First) algorithm. We peek at the task run-queue to find such tasks to eliminate wastage of the slack generated. Based on the outcome of the conducted experiments, the proposed algorithm outperformed or matched the performance of the 2-Phase dynamic task scheduling algorithm all the time.