This paper presents a waveform-matched waveform interpolation (WMWI) technique which enables improved speech analysis over existing WI coders. In WMWI, an accurate representation of speech evolution is produced by extracting critically-sampled pitch periods of a time-warped, constant pitch residual. The technique also offers waveform-matching capabilities by using an inverse warping process to near-perfectly reconstruct the residual. Here, a pitch track optimisation technique is described which ensures the speech residual can be effectively decomposed and quantised. Also, the pitch parameters required to efficiently quantise and recreate the pitch track, on a period-by-period basis, are identified. This allows time-synchrony between the original and decoded signals to be preserved.