Higher order spectral (HOS) techniques, such as the bispectrum, offer robustness to Gaussian noise and the ability to recover phase information. However, their drawbacks, such as the high variance of estimates and the need for long data records, have limited their use in conventional speech processing applications. As in glottal pulse estimation, all existing inverse filtering approaches use second-order statistics, it is of interest to explore the potential of HOS in this area. Using the theory of HOS factorization and the linear bispectrum, it is shown how voiced speech can be modelled as a nonGaussian coloured noise driven system. The linear bispectrum approach can be used to obtain alternative glottal pulse and vocal tract estimates in hybrid Iterative Adaptive Inverse Filtering (hIAIF) and the results are compared with traditional IAIF. Finally, a new technique which involves joint estimation of the glottal pulse and vocal tract followed by inverse filtering is presented. This new technique shows good preliminary results and is much simpler than previous techniques.