Analysis-by-Synthesis LPC (ABS-LPC) based speech cod- ing schemes have been very successful at producing good quality speech below 8Kbit/s. In this paper we report on work to further enhance on the capabilities of ABS-LPC schemes, particularly CELP. Specifically, our attention has been focused on reoptimising the time-varying filter of ABS-LPC schemes by introducing a sequential iterative estimation procedure which extracts the best excitation and filter combination. Also, by adopting a pole-zero filter in place of the all-pole LPC filter a more general approach is introduced which gives better coverage of the speech variations. This new coder, ARMA-CELP, was found to give good objective and subjective results when compared with a standard CELP coder.