This paper considers low-rate waveform interpolation (WI) coding. It compares the existing, common slowly evolving waveform (SEW) quantisation scheme with two new schemes for representing and quantising the SEW. The first scheme uses a minimum phase estimate to reconstruct the SEW whilst the second scheme uses a pulse model whose parameters are implicitly transmitted in the quantised rapidly evolving waveform (REW). These new schemes maintain or reduce the bit rate required for transmission of the SEW. Results indicate that, for low rate WI coding, necessarily coarse SEW magnitude spectrum quantisation limits the contribution of the SEW to perceptual quality. Perceptual tests indicate that avoiding coarse spectral shape quantisation and using a fixed shape model that lends itself to smooth interpolation, maintains the perceptual quality of the synthesized speech. The proposed fixed shape model requires no bits for transmission, allowing a 12 percent reduction in the overall coder bit rate.