Energy-aware task scheduling is critical for real-time embedded systems. Although dynamic power has traditionally been a primary source of processor power consumption, leakage power is becoming increasingly important. In this paper, we present two optimal energy-aware polynomial-time algorithms for scheduling a set of tasks with release times, deadlines and precedence constraints on a single processor with continuous voltages. Our algorithms are guaranteed to minimise the total energy consumption of all tasks while minimising their maximum lateness under two power models: the dynamic power model where the dynamic power dominates the processor power consumption and the dynamic and leakage power model where both dynamic power and leakage power are significant sources of the processor power consumption. The time complexities of both algorithms are O(n³) , where n is the number of tasks.