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Energy efficient communications in ad hoc and sensor wireless networks is a very important topic. We study the problem of creating spanning trees of low cost, where low cost can be viewed in terms of global or local energy efficiency. We refer to the algorithms and techniques presented in the literature, and we show an extension to them, called TDPC (time division path changing), which takes into account both global and local efficiency. We show that these techniques can be applied to existing algorithms, improving the performance, and addressing both needs. We show how it is possible, in general, to cut a trade-off between the two contrasting requests of global and local energy efficiency, by using TDPC with a particular class of algorithms.