This paper presents a new algorithm for high-quality speech coding and demonstrates the advantage of the proposed coder over the conventional CELP algorithm for low rate coding. The paper proposes an empirical but perceptually advantageous framework for voiced speech processing, called Time-Frequency Interpolation (TFI). The general formulation of the TFI technique is given first. Then, a 4.2 Kbps speech coder, based on TFI, is described. The performance of this coder is demonstrated in terms of formal MOS scores. It is shown that the 4.2 Kbps TFI coder is comparable in performance to the 8 Kbps North-American cellular standard IS54 coder and to the 13 Kbps European standard GSM coder.