Exploiting the capabilities offered by the plethora of existing wavelets, together with the powerful set of orthonormal bases provided by wavelet packets, we construct a novel wavelet packet-based set of speech features that is optimized for the task of speaker verification. Our approach differs from previous wavelet-based work, primarily in the wavelet-packet tree design that follows the concept of critical bands, as well as in the particular wavelet basis function that has been used. In comparative experiments, we investigate several alternative speech parameterizations with respect to their usefulness for differentiating among human voices. The experimental results confirm that the proposed speech features outperform Mel-Frequency Cepstral Coefficients (MFCC) and previously used wavelet features on the task of speaker verification. A relative reduction of the equal error rate by 15%, 15% and 8% was observed for the proposed speech features, when compared to the wavelet packet features introduced by Farooq and Datta, the MFCC of Slaney, and the subband based cepstral coefficients of Sarikaya et al., respectively.