We describe new methods of denoising images that combine wavelet shrinkage with properties related to the statistics of quad-trees of wavelet transform values for natural images. They are called tree- adapted wavelet shrinkage (TAWS) methods. The shift-averaged version of TAWS produces denoisings that are comparable to state of the art denoising methods, such as cycle-spin thresholding and the cycle- spin version of the hidden Markov tree method. The nonshift averaged version of TAWS is superior to the classic wavelet shrinkage method, and fits naturally into a signal compression algorithm. These TAWS methods bear some relation to the recently proposed hidden Markov tree methods, but are deterministic rather than probabilistic. They may prove useful in settings where speed is critical and/or signal compression is required.