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We consider wavelet-based self-affine modeling of speech signals for speech compression. We propose two approaches. In the first approach, the self-affine modeling is considered for the representation of speech signal itself. In the second approach, the self-affine modeling is applied for the representation of speech excitation of a linear predictor. In both approaches, error propagation at reconstruction due to the modeling error is avoided by using a causal domain pool. We compare the performance of proposed schemes with that of the GSM 06.10 standard.