This paper proposes a new low rate speech coding algorithm, based on a subband approach. At first, a frame of the incoming signal is fed to a low pass filter, thus yielding the low frequency (LF) part. By subtracting the latter from the incoming signal the high frequency (HF), non-smoothed part is obtained. The HF part is modeled using waveform vector quantisation (VQ), while the LF part is modeled using a spectral estimation method based on a Hankel matrix, its shift invariant property and SVD, called CSE. At the receiver side an adaptive postfiltering based on SVD is performed for the HF part, a simple resynthesis for the LF part, before the two components are added in order to produce the reconstructed signal. Progressive speech compression (variable degree of analysis/synthesis at transmitter/receiver) is thus possible resulting in a variable bit rate scheme. The new method is compared to the CELP algorithm at 4800 bps and is proven of similar quality, in terms of intelligibility and segmental SNR. Moreover, perceptual evaluation tests of the new method were conducted for different bit rates up to 1200 bps and the majority of the evaluators indicated that the technique provides intelligible reconstruction.