This paper examines the information content of the residual error associated with the LPC approach to speech analysis. This is done in the Fourier transform domain. In the ideal case, the magnitude of the residual spectrum is flat, suggesting that the major information component is in the phase. We present results on the relative importance of phase and magnitude by various non-linear processing schemes applied to the residual prior to re-construction in a conventional full RELP system. Included in the experiments are LPC vector quantisation and forward and backward pitch prediction. We show that most of the important information within the residual signal is contained in the phase spectrum. Furthermore, the important components are within a relatively narrow frequency band (0 to 600Hz). It is found that coarse quantisation of these components is sufficient to convey the information critical to the speech re-construction. This leads to a coding scheme based on pitch prediction, an LPC codebook, residual phase and gain with a combined rate of 1520 bits/sec.