Abstract In this paper, we provide a review of LPC parameter quantisation for wideband speech coding as well as evaluate our contributions, namely the switched split vector quantiser (SSVQ) and multi-frame GMM-based block quantiser. We also compare the performance of various quantisation schemes on the two popular LPC parameter representations: line spectral frequencies (LSFs) and immittance spectral pairs (ISPs). Our experimental results indicate that ISPs are superior to LSFs by 1 bit/frame in independent quantiser schemes, such as scalar quantisers; while LSFs are the superior representation for joint vector quantiser schemes. We also derive informal lower bounds, 35 and 36 bits/frame, for the transparent coding of LSFs and ISPs, respectively, via the extrapolation of the operating distortion-rate curve of the unconstrained vector quantiser. Finally, we report and discuss the results of applying the SSVQ with dynamically-weighted distance measure and the multi-frame GMM-based block quantiser, which achieve transparent coding at 42 and 37 bits/frame, respectively, for LSFs. ISPs were found to be inferior to the LSFs by 1 bit/frame. In our comparative study, other quantisation schemes that were investigated include PDF-optimised scalar quantisers, the memoryless Gaussian mixture model-based block quantiser, the split vector quantiser, and the split-multistage vector quantiser with MA predictor from the AMR-WB (ITU-T G.722.2) speech coder.