The aim of speech scrambling algorithms is to transform clear speech into an unintelligible signal so that it is difficult to decrypt it in the absence of the key. Most of the existing speech scrambling algorithms tend to retain considerable residual intelligibility in the scrambled speech and are easy to break. Typically, a speech scrambling algorithm involves permutation of speech segments in time, frequency or time-frequency domain or permutation of transform coefficients of each speech block. The time-frequency algorithms have given very low residual intelligibility and have attracted much attention. We first study the uniform filter bank based time-frequency scrambling algorithm with respect to the block length and number of channels. We use objective distance measures to estimate the departure of the scrambled speech from the clear speech. Simulations indicate that the distance measures increase as we increase the block length and the number of chan­nels. This algorithm derives its security only from the time-frequency segment permutation and it has been estimated that the effective number of permutations which give a low residual intelligibility is much less than the total number of possible permutations. In order to increase the effective number of permutations, we propose a time-frequency scrambling algorithm based on wavelet packets. By using different wavelet packet filter banks at the analysis and synthesis end, we add an extra level of security since the eavesdropper has to choose the correct analysis filter bank, correctly rearrange the time-frequency segments, and choose the correct synthesis bank to get back the original speech signal. Simulations performed with this algorithm give distance measures comparable to those obtained for the uniform filter bank based algorithm. Finally, we introduce the 2-channel perfect reconstruction circular convolution filter bank and give a simple method for its design. The filters designed using this method satisfy the paraunitary properties on a discrete equispaced set of points in the frequency domain.