Broadband reprocessed seismic data from the North West Shelf of Australia were inverted using wavelets estimated with a conventional approach. The inversion method applied was a facies-based inversion, in which the low-frequency model is a product of the inversion process itself, constrained by facies-dependent input trends, the resultant facies distribution, and the match to the seismic. The results identified the presence of a gas reservoir that had recently been confirmed through drilling. The reservoir is thin, with up to 15 ms of maximum thickness. The bandwidth of the seismic data is approximately 5–70 Hz, and the well data used to extract the wavelet used in the inversion are only 400 ms long. As such, there was little control on the lowest frequencies of the wavelet. Different wavelets were subsequently estimated using a variety of new techniques that attempt to address the limitations of short well-log segments and low-frequency seismic. The revised inversion showed greater gas-sand continuity and an extension of the reservoir at one flank. Noise-free synthetic examples indicate that thin-bed delineation can depend on the accuracy of the low-frequency content of the wavelets used for inversion. Underestimation of the low-frequency contents can result in missing thin beds, whereas underestimation of high frequencies can introduce false thin beds. Therefore, it is very important to correctly capture the full frequency content of the seismic data in terms of the amplitude and phase spectra of the estimated wavelets, which subsequently leads to a more accurate thin-bed reservoir characterization through inversion.