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Smart energy management is an important problem in Smart Grid network, and demand response (DR) is one of the key enabling technologies. If each home uses automated demand response which would opportunistically schedule devices that are flexible to run at any time in a large time window, towards the slots with lower electricity prices, rebound peak at these slots may happen. We address the potential problems of automated DR algorithms, and provide possible solutions. We illustrate why a rebound peak is possible via the insights we obtain from the mathematically proven optimal automated DR algorithm. We show that a system of multiple homes and utility company has the lowest overall cost if the energy usage is flat over time, study multiple approaches for leveraging the rebound peak, and accordingly propose algorithms for DR at each home. Effectiveness of the approaches is verified by numerical results.