Wavelet decomposition of data has been used with success for data compression in a large class of signals. The wavelet packets representation is a decomposition that includes as a special case the wavelet transform. In this scheme, wavelet packets are assembled as a representation of the signal. There exist a large number of possible wavelet combinations for each signal. An adaptation scheme based on the genetic optimization method is presented for determining an optimal representation for data compression. Experiment results using real data as well as autoregressive random processes are used to compare the performance of the adapted packets and the wavelet transform.