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We tackle the problem of reducing power consumption in IP-over-WDM networks, targeting the power-aware logical topology design (LTD). Unlike the previous work in the literature, our solution reduces the power consumption with consideration of the cost (in terms of reconfigured traffic) incurred when the network is reconfigured. We first formulate the LTD with reconfiguration costs as an optimization problem. Then, we present three heuristics to effectively solve it. We compare our algorithms over an extensive set of networks and scenarios. Results indicate that our algorithms are effective in reducing power consumption while limiting the amount of traffic that is reconfigured. Moreover, we show that the input parameters are intuitive and easy to set, which makes our algorithms more practical.