Monthly rainfall in the wetter western half of Tasmania was relatively poorly observed in the early to middle parts of the 20th century, and this causes a marked inhomogeneity in the operational gridded monthly rainfall analyses generated by the Australian Bureau of Meteorology up until the end of 2009. These monthly rainfall analyses were generated for the period 1900 to 2009 in two forms; a national analysis at 0.25° latitude-longitude resolution, and a southeastern Australia regional analysis at 0.1° resolution. For any given month, they used all the monthly data from the standard Bureau rainfall gauge network available in the Australian Data Archive for Meteorology. Since this network has changed markedly since Federation (1901), there is obvious scope for network-derived inhomogeneities in the analyses. In this study, we show that the topography-resolving techniques of the new Australian Water Availability Project analyses, adopted as the official operational analyses from the start of 2010, substantially diminish those inhomogeneities, while using largely the same observation network. One result is an improved characterisation of recent rainfall declines across Tasmania. The new analyses are available at two resolutions, 0.25° and 0.05°.