In this paper, we optimize the use of existing DSL low-power sleeping modes (L2 and L3) in order to improve the energy efficiency of DSL access networks. Given that switching on a DSL line can cause instability by increasing the amount of time-varying crosstalk in the cable bundle, and that it takes energy and time to switch a DSL line on and off , we develop a method to optimally choose the appropriate sleeping state based on the line and traffic characteristics. We further develop and prove the structural properties of the optimal policy for switching to the appropriate sleeping state, allowing transitions between submodes with different power and transmit rate characteristics. We also present techniques that guarantee stable sleep mode operation. Using a realistic DSL simulator, we demonstrate the three-way tradeoff among energy consumption, delay performance, and stability. The increased flexibility of control introduced by our approach improves the energy-delay Pareto optimal tradeoff, and results in a more energy efficient and stable DSL operation compared to existing power saving policies.