In this paper we present novel techniques to adapt conventional wavelet transforms to follow locally oriented features found in images. We introduce a shift operator before each step in a lifting implementation of the DWT. The best shifts are estimated by minimizing the high-pass coefficient energy and then used in both the prediction and update lifting steps. To approximate the asymptotically optimal rate-distortion performance of a piece-wise regular function more closely, we adopt a packet wavelet decomposition. Experimental results obtained integrating the proposed transform into the JPEG2000 codec show improvements in both visual and objective tests, allowing for a "better" representation of the edges at very-low rates. Very recently, some related ideas have been presented by other authors. The most distinctive features of this paper include a more flexible packet wavelet decomposition structure and a comparison between subband- and image-domain shifting operators.