Switching off a DSL line to a low-power sleeping state is becoming an important method to enhance energy efficiency of DSL broadband access networks. Although a low-power (L2) state and an off (L3) state are already defined in DSL standards, they have not been fully exploited due to concern about the resulting time-varying crosstalk. In this paper, we develop a method to optimally choose the appropriate sleeping state based on the modem's switching cost characteristics and the power consumption incurred during each sleeping state. We further develop the optimal policy for switching to the appropriate sleeping state, allowing transitions between operating modes with different power and transmit rate. Numerical results on our realistic DSL simulator show that more flexibility in control, introduced by our approach, improves the energy-delay Pareto optimal tradeoff, and results in a more energy efficient and stable DSL system compared to the existing power saving policies.