This paper describes an effective and efficient time domain speech encoding technique that has an appealing low complexity, and produces toll quality speech at rates below 16 kbits/s. The proposed coder uses linear predictive techniques to remove the short-time correlation in the speech signal. The remaining (residual) information is then modeled by a low bit rate reduced excitation sequence that, when applied to the time-varying model filter, produces a signal that is "close" to the reference speech signal. The procedure for finding the optimal constrained excitation signal incorporates the solution of a few strongly coupled sets of linear equations and is of moderate complexity compared to competing coding systems such as adaptive transform coding and multipulse excitation coding. The paper describes the novel coding idea and the procedure for finding the excitation sequence. We then show that the coding procedure can be considered as an "optimized" baseband coder with spectral folding as high-frequency regeneration technique. The effect of various analysis parameters on the quality of the reconstructed speech is investigated using both objective and subjective tests. Further, modifications of the basic algorithm, and their impact on both the quality of the reconstructed speech signal and the complexity of the encoding algorithm, are discussed. Using the generalized baseband coder formulation, we demonstrate that under reasonable assumptions concerning the weighting filter, an attractive low-complexity/high-quality coder can be obtained.