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In multipulse LPC speech coding, there are a number of important issues which need to be addressed. The purpose of this paper is to report some of our work related to two of these issues. The first pertains to how one measures the quality of the synthetic speech for a given set of multipulse parameters. In this paper, we present a general set of frequency domain weighting functions which may incorporate various spectral characterizations of the speech. The second issue relates to how one determines the optimal set of pulse positions for a given set of of LPC filter coefficients. Current methods involve a sequential procedure, which is suboptimal compared with simultaneous positioning of pulses throughout an entire analysis frame. We therefore discuss an algorithm for simultaneous pulse positioning based on Pisarenko's harmonic decomposition.