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, peaks at these slots may happen. We denote such peaks as rebound peaks. We address the potential rebound peak problems of automated DR algorithms, and provide possible solutions. We illustrate why a rebound peak is possible via the insights we obtain from the optimal automated DR algorithm. We show that if the utility electricity supply cost is assumed to be a homogeneous function in the energy consumption over a certain time span, a system of multiple homes and utility company has the lowest total electricity supply cost if the electricity consumption from all the homes is flat over the time span. We study multiple approaches to reduce the rebound peak, and accordingly propose algorithms for DR at each home. Effectiveness of the approaches is verified by numerical results.