This paper outlines a new algorithm for searching minimum bit rate wavelet packet representations in a high quality wavelet-based perceptual audio coder. The algorithm claims wavelet tree and prototype filter adaptation attending to a perceptual cost function. To achieve such adaptive structure, a periodized wavelet packet transform is performed for each audio frame. After the transform, the encoder employs scalar adaptive quantization, controlled by a psycho-acoustic model in the wavelet domain, followed by entropy coding and bit packing. An adaptive Huffman algorithm that assumes Laplacian distributions for wavelet coefficients is used for entropy coding. A relevant feature of our coder is the method to translate the psycho-acoustic information to the wavelet domain, which allows using orthonormal wavelets of any compact support. Experimental results indicate that our coder ensures 'transparent' coding of monophonic CD audio signals at bit rates lower than 64 kb/s for all the test signals.