Broadband re-processed seismic data from the NW Shelf of Australia were inverted using a standard approach to wavelet estimation. The inversion method applied was a facies-based deterministic inversion where 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 only a short well log was available to extract the wavelets. As such there was little control on the lowest frequencies of the wavelet. Wavelets were then 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 produced similar results but showed greater continuity and an extension of the reservoir at one flank. These differences could be traced back to the low frequency component of the inversion results and suggest that subtle variations in the low frequency component of wavelets can have an impact on seismic reservoir characterisation of thin beds.