Slowdown based on dynamic voltage scaling (DVS) provides the ability to perform an energy-delay tradeoff in the system. Non-preemptive scheduling becomes an integral part of systems where resource characteristics makes preemption undesirable or impossible. We address the problem of energy efficient scheduling of non-preemptive tasks based on the Earliest Deadline First (EDF) scheduling policy. We present the stack based slowdown algorithm that builds upon the optimal feasibility test for non-preemptive systems. We also propose a dynamic slack reclamation policy to further enhance energy savings. Simulation results show on an average 15% energy savings using static slowdown factors and 20% savings with dynamic slowdown, over known slowdown techniques.