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In this study novel data hiding methods that embed secret data during mixed excitation linear prediction (MELP) coding of the speech signal are proposed. The secret data bits are hidden by using quantisation index modulation (QIM) which is carried out in the multistage vector quantisation (MSVQ) of line spectral frequencies (LSF) parameters. The distortion rates, introduced by the proposed data hiding methods, are compared with that of a previously published dither-like data hiding method by employing tests performed on the speech files selected from NTIMIT database. Weighted Euclidian distances and spectral distortion are calculated as objective distortion quality metrics, whereas perceptual evaluation of speech quality, PESQ P.862, which tries to mimic mean opinion scores, is used to give subjective listening test results. After the calculation of objective and subjective quality metrics, it is determined that the methods with QIM at the third and fourth stages of the MSVQ distort speech only as much as that resulting from a 10-3 bit error rated (BER) additive white Gaussian noise (AWGN) channel. Later, steganographic strengths of some selected QIM methods are elaborated by the steganalysis methods trained with the computed chaotic features. According to the steganalysis results, methods that apply QIM on the third and fourth indexes of MELP-MSVQ assure both lower distortion and better steganographic imperceptibility.