To address the problem of non-stationarity, the double tree algorithm was proposed by Herley, Kovačević, Ramchandran and Vetterli [HKRV93]. The double tree finds the best wavelet packet basis for a hierarchy of binary segmentations of the signal. The overall basis search identifies the most efficient dyadic segmentation and corresponding wavelet packet expansions for the segments. However, the double tree does not exploit the full potential of the joint space and frequency library. The insufficiency results from the asymmetric treatment of the space and frequency operations in the tree cascade. We will show that image compression performance improves when the basis search uses a graph to better exploit the space and frequency library, rather than the double tree.