In the search for adaptive representation of speech signals, the Wavelet Packet Decomposition (WPD) has been proved to be a efficient tool because of its frequency adaptation skills through the best basis search algorithm. The entropic minimization of this algorithm is bounded by two artifacts : the dyadic structure of the decomposition and the lack of temporal segmentation. We propose here a low cost extended tree in the WPD which improves the best basis search by reducing the entropy of the base and which is still compatible with the classical WPD. The decomposition also allows perfect reconstruction. The entropic test is updated to take into account the new basis. The preliminary use of a temporal segmentation, based on the Local Entropic Criterion highly improves the entropic gain of the global analysis. The results are shown on experimental speech signals comparing the gain of our scheme versus a usual WPD.